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Expand $(x + 6)(x + 9)$ . What is the coefficient of $x$ ?
What is the constant term of $(x + 9)(x^2 + 1x + 6)$ ?
A polynomial of degree 5 is multiplied by a polynomial of degree 5. What is the degree of the product?
Find the coefficient of $x^2$ in $(1 + x)^{ 10 }$ .
Find the coefficient of $x$ in $(x + 4)^{ 4 }$ .
In $(2x + 2)^2 = 4x^2 + kx + 4$ , what is $k$ ?
$x^2 + 36 = 0$ . Enter the solution with positive imaginary part.
$x^2 - 4x + 20 = 0$ . Enter the solution with positive imaginary part.
Find the discriminant of $1x^2 + 7x + 4 = 0$ .
Describe the end behavior of $f(x) = 7x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 3x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 3x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 8x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 4x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 7x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 5x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 5x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 7x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 2x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 5x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 2x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 9x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 4x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 3x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 6x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 8x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 8x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 9x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 4x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 6x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 6x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 2x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 9x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -9x^{ 6 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -8x^{ 4 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -6x^{ 4 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -9x^{ 2 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -2x^{ 6 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -6x^{ 2 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -3x^{ 4 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -3x^{ 2 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -2x^{ 2 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -4x^{ 2 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -8x^{ 6 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -9x^{ 4 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -3x^{ 6 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -4x^{ 6 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -8x^{ 2 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -7x^{ 6 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -4x^{ 4 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -5x^{ 6 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -6x^{ 6 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -7x^{ 4 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -5x^{ 4 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -2x^{ 4 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -5x^{ 2 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = -7x^{ 2 }$ .
1. As $x \to \pm\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
$p(x) = 7x^2 - 9x^5 + 9$ . What is the leading coefficient of $p$ ?
Find all the zeros of $p(x) = (x - 4)(x + 2)^2$ .
$p(x) = (x - 4)^2(x + 9)$ . What does the graph of $p$ do at $x = 4$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 5)^2(x + 1)$ . What does the graph of $p$ do at $x = 5$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 7)^2(x + 4)$ . What does the graph of $p$ do at $x = 7$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 4)^2(x + 3)$ . What does the graph of $p$ do at $x = 4$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 5)^2(x + 2)$ . What does the graph of $p$ do at $x = 5$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 7)^2(x + 7)$ . What does the graph of $p$ do at $x = 7$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 2)^2(x + 6)$ . What does the graph of $p$ do at $x = 2$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 7)^2(x + 8)$ . What does the graph of $p$ do at $x = 7$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 2)^2(x + 7)$ . What does the graph of $p$ do at $x = 2$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 8)^2(x + 6)$ . What does the graph of $p$ do at $x = 8$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 8)^2(x + 1)$ . What does the graph of $p$ do at $x = 8$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 4)^2(x + 8)$ . What does the graph of $p$ do at $x = 4$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 6)^2(x + 2)$ . What does the graph of $p$ do at $x = 6$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 8)^2(x + 2)$ . What does the graph of $p$ do at $x = 8$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 1)^2(x + 7)$ . What does the graph of $p$ do at $x = 1$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 5)^2(x + 6)$ . What does the graph of $p$ do at $x = 5$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 3)^2(x + 9)$ . What does the graph of $p$ do at $x = 3$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 2)^2(x + 9)$ . What does the graph of $p$ do at $x = 2$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 7)^2(x + 3)$ . What does the graph of $p$ do at $x = 7$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 2)^2(x + 5)$ . What does the graph of $p$ do at $x = 2$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 4)^2(x + 1)$ . What does the graph of $p$ do at $x = 4$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 8)^2(x + 8)$ . What does the graph of $p$ do at $x = 8$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 3)^2(x + 8)$ . What does the graph of $p$ do at $x = 3$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 1)^2(x + 3)$ . What does the graph of $p$ do at $x = 1$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 1)^2(x + 4)$ . What does the graph of $p$ do at $x = 1$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 9)^2(x + 3)$ . What does the graph of $p$ do at $x = 9$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 9)^2(x + 6)$ . What does the graph of $p$ do at $x = 9$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 9)^2(x + 9)$ . What does the graph of $p$ do at $x = 9$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 8)^2(x + 4)$ . What does the graph of $p$ do at $x = 8$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 6)^2(x + 6)$ . What does the graph of $p$ do at $x = 6$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 7)^2(x + 1)$ . What does the graph of $p$ do at $x = 7$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 8)^2(x + 5)$ . What does the graph of $p$ do at $x = 8$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 9)^2(x + 1)$ . What does the graph of $p$ do at $x = 9$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 6)^2(x + 9)$ . What does the graph of $p$ do at $x = 6$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 5)^2(x + 3)$ . What does the graph of $p$ do at $x = 5$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 6)^2(x + 1)$ . What does the graph of $p$ do at $x = 6$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 2)^2(x + 3)$ . What does the graph of $p$ do at $x = 2$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 6)^2(x + 4)$ . What does the graph of $p$ do at $x = 6$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 4)^2(x + 6)$ . What does the graph of $p$ do at $x = 4$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 9)^2(x + 2)$ . What does the graph of $p$ do at $x = 9$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 6)^2(x + 7)$ . What does the graph of $p$ do at $x = 6$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 4)^2(x + 7)$ . What does the graph of $p$ do at $x = 4$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 9)^2(x + 7)$ . What does the graph of $p$ do at $x = 9$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 3)^2(x + 4)$ . What does the graph of $p$ do at $x = 3$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 1)^2(x + 8)$ . What does the graph of $p$ do at $x = 1$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 4)^2(x + 5)$ . What does the graph of $p$ do at $x = 4$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 3)^2(x + 1)$ . What does the graph of $p$ do at $x = 3$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 1)^2(x + 2)$ . What does the graph of $p$ do at $x = 1$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 4)^2(x + 4)$ . What does the graph of $p$ do at $x = 4$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
$p(x) = (x - 3)^2(x + 5)$ . What does the graph of $p$ do at $x = 3$ ?
1. It touches the x-axis and turns back
2. It crosses the x-axis
3. It does not reach the x-axis
Divide: $\dfrac{x^2 + 13x + 42}{x + 6}$ . Enter the quotient.
Divide $x^3 - 1$ by $x - 1$ . Enter the quotient.
Find the remainder when $x^2 + 4x + 1$ is divided by $x - 4$ .
What is the remainder when $p(x) = x^3 - 5x + 7$ is divided by $x - 3$ ?
Is $x - 3$ a factor of $p(x) = x^2 - 7x + 12$ ?
1. Yes, because $p(3) = 0$
2. No, because $p(-3) \ne 0$
3. Only if dividing $p(x)$ by $x - 3$ leaves the remainder 3
Is $x - 5$ a factor of $p(x) = x^2 - 8x + 15$ ?
1. Yes, because $p(5) = 0$
2. No, because $p(-5) \ne 0$
3. Only if dividing $p(x)$ by $x - 5$ leaves the remainder 5
Is $x - 1$ a factor of $p(x) = x^2 - 6x + 5$ ?
1. Yes, because $p(1) = 0$
2. No, because $p(-1) \ne 0$
3. Only if dividing $p(x)$ by $x - 1$ leaves the remainder 1
Is $x - 3$ a factor of $p(x) = x^2 - 9x + 18$ ?
1. Yes, because $p(3) = 0$
2. No, because $p(-3) \ne 0$
3. Only if dividing $p(x)$ by $x - 3$ leaves the remainder 3
Is $x - 6$ a factor of $p(x) = x^2 - 7x + 6$ ?
1. Yes, because $p(6) = 0$
2. No, because $p(-6) \ne 0$
3. Only if dividing $p(x)$ by $x - 6$ leaves the remainder 6
Is $x - 1$ a factor of $p(x) = x^2 - 4x + 3$ ?
1. Yes, because $p(1) = 0$
2. No, because $p(-1) \ne 0$
3. Only if dividing $p(x)$ by $x - 1$ leaves the remainder 1
Is $x - 2$ a factor of $p(x) = x^2 - 5x + 6$ ?
1. Yes, because $p(2) = 0$
2. No, because $p(-2) \ne 0$
3. Only if dividing $p(x)$ by $x - 2$ leaves the remainder 2
Is $x - 6$ a factor of $p(x) = x^2 - 9x + 18$ ?
1. Yes, because $p(6) = 0$
2. No, because $p(-6) \ne 0$
3. Only if dividing $p(x)$ by $x - 6$ leaves the remainder 6
Is $x - 2$ a factor of $p(x) = x^2 - 6x + 8$ ?
1. Yes, because $p(2) = 0$
2. No, because $p(-2) \ne 0$
3. Only if dividing $p(x)$ by $x - 2$ leaves the remainder 2
Is $x - 4$ a factor of $p(x) = x^2 - 6x + 8$ ?
1. Yes, because $p(4) = 0$
2. No, because $p(-4) \ne 0$
3. Only if dividing $p(x)$ by $x - 4$ leaves the remainder 4
Is $x - 5$ a factor of $p(x) = x^2 - 9x + 20$ ?
1. Yes, because $p(5) = 0$
2. No, because $p(-5) \ne 0$
3. Only if dividing $p(x)$ by $x - 5$ leaves the remainder 5
Is $x - 1$ a factor of $p(x) = x^2 - 7x + 6$ ?
1. Yes, because $p(1) = 0$
2. No, because $p(-1) \ne 0$
3. Only if dividing $p(x)$ by $x - 1$ leaves the remainder 1
Is $x - 6$ a factor of $p(x) = x^2 - 10x + 24$ ?
1. Yes, because $p(6) = 0$
2. No, because $p(-6) \ne 0$
3. Only if dividing $p(x)$ by $x - 6$ leaves the remainder 6
Is $x - 3$ a factor of $p(x) = x^2 - 4x + 3$ ?
1. Yes, because $p(3) = 0$
2. No, because $p(-3) \ne 0$
3. Only if dividing $p(x)$ by $x - 3$ leaves the remainder 3
Is $x - 4$ a factor of $p(x) = x^2 - 7x + 12$ ?
1. Yes, because $p(4) = 0$
2. No, because $p(-4) \ne 0$
3. Only if dividing $p(x)$ by $x - 4$ leaves the remainder 4
Is $x - 5$ a factor of $p(x) = x^2 - 6x + 5$ ?
1. Yes, because $p(5) = 0$
2. No, because $p(-5) \ne 0$
3. Only if dividing $p(x)$ by $x - 5$ leaves the remainder 5
Is $x - 1$ a factor of $p(x) = x^2 - 3x + 2$ ?
1. Yes, because $p(1) = 0$
2. No, because $p(-1) \ne 0$
3. Only if dividing $p(x)$ by $x - 1$ leaves the remainder 1
Is $x - 2$ a factor of $p(x) = x^2 - 3x + 2$ ?
1. Yes, because $p(2) = 0$
2. No, because $p(-2) \ne 0$
3. Only if dividing $p(x)$ by $x - 2$ leaves the remainder 2
Is $x - 3$ a factor of $p(x) = x^2 - 5x + 6$ ?
1. Yes, because $p(3) = 0$
2. No, because $p(-3) \ne 0$
3. Only if dividing $p(x)$ by $x - 3$ leaves the remainder 3
Is $x - 2$ a factor of $p(x) = x^2 - 8x + 12$ ?
1. Yes, because $p(2) = 0$
2. No, because $p(-2) \ne 0$
3. Only if dividing $p(x)$ by $x - 2$ leaves the remainder 2
Is $x - 5$ a factor of $p(x) = x^2 - 7x + 10$ ?
1. Yes, because $p(5) = 0$
2. No, because $p(-5) \ne 0$
3. Only if dividing $p(x)$ by $x - 5$ leaves the remainder 5
Is $x - 1$ a factor of $p(x) = x^2 - 5x + 4$ ?
1. Yes, because $p(1) = 0$
2. No, because $p(-1) \ne 0$
3. Only if dividing $p(x)$ by $x - 1$ leaves the remainder 1
Is $x - 4$ a factor of $p(x) = x^2 - 5x + 4$ ?
1. Yes, because $p(4) = 0$
2. No, because $p(-4) \ne 0$
3. Only if dividing $p(x)$ by $x - 4$ leaves the remainder 4
Is $x - 5$ a factor of $p(x) = x^2 - 11x + 30$ ?
1. Yes, because $p(5) = 0$
2. No, because $p(-5) \ne 0$
3. Only if dividing $p(x)$ by $x - 5$ leaves the remainder 5
Is $x - 6$ a factor of $p(x) = x^2 - 11x + 30$ ?
1. Yes, because $p(6) = 0$
2. No, because $p(-6) \ne 0$
3. Only if dividing $p(x)$ by $x - 6$ leaves the remainder 6
Is $x - 2$ a factor of $p(x) = x^2 - 7x + 10$ ?
1. Yes, because $p(2) = 0$
2. No, because $p(-2) \ne 0$
3. Only if dividing $p(x)$ by $x - 2$ leaves the remainder 2
Is $x - 6$ a factor of $p(x) = x^2 - 8x + 12$ ?
1. Yes, because $p(6) = 0$
2. No, because $p(-6) \ne 0$
3. Only if dividing $p(x)$ by $x - 6$ leaves the remainder 6
Is $x - 4$ a factor of $p(x) = x^2 - 10x + 24$ ?
1. Yes, because $p(4) = 0$
2. No, because $p(-4) \ne 0$
3. Only if dividing $p(x)$ by $x - 4$ leaves the remainder 4
Is $x - 4$ a factor of $p(x) = x^2 - 9x + 20$ ?
1. Yes, because $p(4) = 0$
2. No, because $p(-4) \ne 0$
3. Only if dividing $p(x)$ by $x - 4$ leaves the remainder 4
Is $x - 3$ a factor of $p(x) = x^2 - 8x + 15$ ?
1. Yes, because $p(3) = 0$
2. No, because $p(-3) \ne 0$
3. Only if dividing $p(x)$ by $x - 3$ leaves the remainder 3
For which value of $k$ is $x - 2$ a factor of $x^2 + kx + 4$ ?
$x = 4$ is a zero of $p(x) = x^3 - 4x^2 - 1x + 4$ . Find all the zeros of $p$ .
Divide $p(x) = x^3 - 2x^2 - 9x + 18$ by $x - 2$ . What is the quotient?
You know that $2$ is a zero of a cubic $p(x)$ . Put the steps for finding all its zeros in order.
- Check that $p(2) = 0$
- Divide $p(x)$ by $x - 2$
- Solve the quadratic quotient $= 0$
- List $2$ with the solutions of the quadratic
You know that $4$ is a zero of a cubic $p(x)$ . Put the steps for finding all its zeros in order.
- Check that $p(4) = 0$
- Divide $p(x)$ by $x - 4$
- Solve the quadratic quotient $= 0$
- List $4$ with the solutions of the quadratic
You know that $5$ is a zero of a cubic $p(x)$ . Put the steps for finding all its zeros in order.
- Check that $p(5) = 0$
- Divide $p(x)$ by $x - 5$
- Solve the quadratic quotient $= 0$
- List $5$ with the solutions of the quadratic
You know that $3$ is a zero of a cubic $p(x)$ . Put the steps for finding all its zeros in order.
- Check that $p(3) = 0$
- Divide $p(x)$ by $x - 3$
- Solve the quadratic quotient $= 0$
- List $3$ with the solutions of the quadratic
You know that $1$ is a zero of a cubic $p(x)$ . Put the steps for finding all its zeros in order.
- Check that $p(1) = 0$
- Divide $p(x)$ by $x - 1$
- Solve the quadratic quotient $= 0$
- List $1$ with the solutions of the quadratic
You know that $6$ is a zero of a cubic $p(x)$ . Put the steps for finding all its zeros in order.
- Check that $p(6) = 0$
- Divide $p(x)$ by $x - 6$
- Solve the quadratic quotient $= 0$
- List $6$ with the solutions of the quadratic
Use an identity to compute $33^2 - 27^2$ .
$x^3 + 64 = (x + 4)(x^2 + bx + 16)$ . Find $b$ .
Use $(1 - r)(1 + r + r^2 + \dots + r^{n-1}) = 1 - r^n$ to compute $1 + 2 + 4 + \dots + 2^{ 4 }$ .
A polynomial with real coefficients has the zero $4 + 4i$ . Which other number must be a zero?
1. $4 - 4i$
2. $-4 - 4i$
3. $-4 + 4i$
A polynomial with real coefficients has the zero $8 + 7i$ . Which other number must be a zero?
1. $8 - 7i$
2. $-8 - 7i$
3. $-8 + 7i$
A polynomial with real coefficients has the zero $4 + 5i$ . Which other number must be a zero?
1. $4 - 5i$
2. $-4 - 5i$
3. $-4 + 5i$
A polynomial with real coefficients has the zero $6 + 5i$ . Which other number must be a zero?
1. $6 - 5i$
2. $-6 - 5i$
3. $-6 + 5i$
A polynomial with real coefficients has the zero $6 + 2i$ . Which other number must be a zero?
1. $6 - 2i$
2. $-6 - 2i$
3. $-6 + 2i$
A polynomial with real coefficients has the zero $2 + 1i$ . Which other number must be a zero?
1. $2 - 1i$
2. $-2 - 1i$
3. $-2 + 1i$
A polynomial with real coefficients has the zero $8 + 8i$ . Which other number must be a zero?
1. $8 - 8i$
2. $-8 - 8i$
3. $-8 + 8i$
A polynomial with real coefficients has the zero $5 + 4i$ . Which other number must be a zero?
1. $5 - 4i$
2. $-5 - 4i$
3. $-5 + 4i$
A polynomial with real coefficients has the zero $6 + 1i$ . Which other number must be a zero?
1. $6 - 1i$
2. $-6 - 1i$
3. $-6 + 1i$
A polynomial with real coefficients has the zero $4 + 9i$ . Which other number must be a zero?
1. $4 - 9i$
2. $-4 - 9i$
3. $-4 + 9i$
A polynomial with real coefficients has the zero $5 + 9i$ . Which other number must be a zero?
1. $5 - 9i$
2. $-5 - 9i$
3. $-5 + 9i$
A polynomial with real coefficients has the zero $9 + 8i$ . Which other number must be a zero?
1. $9 - 8i$
2. $-9 - 8i$
3. $-9 + 8i$
A polynomial with real coefficients has the zero $2 + 9i$ . Which other number must be a zero?
1. $2 - 9i$
2. $-2 - 9i$
3. $-2 + 9i$
A polynomial with real coefficients has the zero $3 + 9i$ . Which other number must be a zero?
1. $3 - 9i$
2. $-3 - 9i$
3. $-3 + 9i$
A polynomial with real coefficients has the zero $5 + 6i$ . Which other number must be a zero?
1. $5 - 6i$
2. $-5 - 6i$
3. $-5 + 6i$
A polynomial with real coefficients has the zero $6 + 4i$ . Which other number must be a zero?
1. $6 - 4i$
2. $-6 - 4i$
3. $-6 + 4i$
A polynomial with real coefficients has the zero $4 + 6i$ . Which other number must be a zero?
1. $4 - 6i$
2. $-4 - 6i$
3. $-4 + 6i$
A polynomial with real coefficients has the zero $1 + 5i$ . Which other number must be a zero?
1. $1 - 5i$
2. $-1 - 5i$
3. $-1 + 5i$
A polynomial with real coefficients has the zero $6 + 7i$ . Which other number must be a zero?
1. $6 - 7i$
2. $-6 - 7i$
3. $-6 + 7i$
A polynomial with real coefficients has the zero $1 + 2i$ . Which other number must be a zero?
1. $1 - 2i$
2. $-1 - 2i$
3. $-1 + 2i$
A polynomial with real coefficients has the zero $2 + 3i$ . Which other number must be a zero?
1. $2 - 3i$
2. $-2 - 3i$
3. $-2 + 3i$
A polynomial with real coefficients has the zero $9 + 5i$ . Which other number must be a zero?
1. $9 - 5i$
2. $-9 - 5i$
3. $-9 + 5i$
A polynomial with real coefficients has the zero $2 + 4i$ . Which other number must be a zero?
1. $2 - 4i$
2. $-2 - 4i$
3. $-2 + 4i$
A polynomial with real coefficients has the zero $9 + 6i$ . Which other number must be a zero?
1. $9 - 6i$
2. $-9 - 6i$
3. $-9 + 6i$
A polynomial with real coefficients has the zero $7 + 6i$ . Which other number must be a zero?
1. $7 - 6i$
2. $-7 - 6i$
3. $-7 + 6i$
A polynomial with real coefficients has the zero $5 + 2i$ . Which other number must be a zero?
1. $5 - 2i$
2. $-5 - 2i$
3. $-5 + 2i$
A polynomial with real coefficients has the zero $5 + 8i$ . Which other number must be a zero?
1. $5 - 8i$
2. $-5 - 8i$
3. $-5 + 8i$
A polynomial with real coefficients has the zero $8 + 3i$ . Which other number must be a zero?
1. $8 - 3i$
2. $-8 - 3i$
3. $-8 + 3i$
A polynomial with real coefficients has the zero $4 + 8i$ . Which other number must be a zero?
1. $4 - 8i$
2. $-4 - 8i$
3. $-4 + 8i$
A polynomial with real coefficients has the zero $2 + 5i$ . Which other number must be a zero?
1. $2 - 5i$
2. $-2 - 5i$
3. $-2 + 5i$
A polynomial with real coefficients has the zero $1 + 9i$ . Which other number must be a zero?
1. $1 - 9i$
2. $-1 - 9i$
3. $-1 + 9i$
A polynomial with real coefficients has the zero $9 + 3i$ . Which other number must be a zero?
1. $9 - 3i$
2. $-9 - 3i$
3. $-9 + 3i$
A polynomial with real coefficients has the zero $3 + 1i$ . Which other number must be a zero?
1. $3 - 1i$
2. $-3 - 1i$
3. $-3 + 1i$
A polynomial with real coefficients has the zero $2 + 7i$ . Which other number must be a zero?
1. $2 - 7i$
2. $-2 - 7i$
3. $-2 + 7i$
A polynomial with real coefficients has the zero $6 + 9i$ . Which other number must be a zero?
1. $6 - 9i$
2. $-6 - 9i$
3. $-6 + 9i$
A polynomial with real coefficients has the zero $1 + 1i$ . Which other number must be a zero?
1. $1 - 1i$
2. $-1 - 1i$
3. $-1 + 1i$
A polynomial with real coefficients has the zero $9 + 2i$ . Which other number must be a zero?
1. $9 - 2i$
2. $-9 - 2i$
3. $-9 + 2i$
A polynomial with real coefficients has the zero $2 + 2i$ . Which other number must be a zero?
1. $2 - 2i$
2. $-2 - 2i$
3. $-2 + 2i$
A polynomial with real coefficients has the zero $3 + 7i$ . Which other number must be a zero?
1. $3 - 7i$
2. $-3 - 7i$
3. $-3 + 7i$
A polynomial with real coefficients has the zero $8 + 2i$ . Which other number must be a zero?
1. $8 - 2i$
2. $-8 - 2i$
3. $-8 + 2i$
A polynomial with real coefficients has the zero $7 + 4i$ . Which other number must be a zero?
1. $7 - 4i$
2. $-7 - 4i$
3. $-7 + 4i$
A polynomial with real coefficients has the zero $9 + 1i$ . Which other number must be a zero?
1. $9 - 1i$
2. $-9 - 1i$
3. $-9 + 1i$
A polynomial with real coefficients has the zero $8 + 4i$ . Which other number must be a zero?
1. $8 - 4i$
2. $-8 - 4i$
3. $-8 + 4i$
A polynomial with real coefficients has the zero $6 + 6i$ . Which other number must be a zero?
1. $6 - 6i$
2. $-6 - 6i$
3. $-6 + 6i$
A polynomial with real coefficients has the zero $8 + 9i$ . Which other number must be a zero?
1. $8 - 9i$
2. $-8 - 9i$
3. $-8 + 9i$
A polynomial with real coefficients has the zero $4 + 2i$ . Which other number must be a zero?
1. $4 - 2i$
2. $-4 - 2i$
3. $-4 + 2i$
A polynomial with real coefficients has the zero $9 + 7i$ . Which other number must be a zero?
1. $9 - 7i$
2. $-9 - 7i$
3. $-9 + 7i$
A polynomial with real coefficients has the zero $3 + 2i$ . Which other number must be a zero?
1. $3 - 2i$
2. $-3 - 2i$
3. $-3 + 2i$
A polynomial with real coefficients has the zero $7 + 2i$ . Which other number must be a zero?
1. $7 - 2i$
2. $-7 - 2i$
3. $-7 + 2i$
A polynomial with real coefficients has the zero $3 + 4i$ . Which other number must be a zero?
1. $3 - 4i$
2. $-3 - 4i$
3. $-3 + 4i$
How many real zeros does $x^2 + 5x + 10$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 4x + 9$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 2x + 20$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 6$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 1x + 1$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 5x + 12$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 6x + 14$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 8$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 4x + 13$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 6x + 12$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 15$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 5x + 7$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 6x + 15$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 5x + 8$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 18$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 1x + 4$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 2x + 10$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 9$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 1x + 10$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 2x + 18$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 2x + 9$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 4x + 19$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 2x + 16$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 6x + 20$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 20$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 2x + 8$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 4x + 17$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 2x + 15$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 14$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 1x + 18$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 4x + 15$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 1x + 3$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 2x + 12$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 19$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 4$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 13$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 5x + 16$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 4x + 20$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 4x + 10$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 1x + 16$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 5x + 13$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 6x + 11$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 1x + 8$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 3$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 4x + 5$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 1x + 13$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 6x + 10$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 1x + 20$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 3x + 5$ have?
1. Two
2. One
3. None: two complex zeros
How many real zeros does $x^2 + 1x + 12$ have?
1. Two
2. One
3. None: two complex zeros
Solve $x^2 - 8x + 25 = 0$ . Type each solution as $a + bi$ .

Answers

$15$
$54$
$10$
$45$
$256$
$8$
$6 i$
$2 + 4 i$
$33$
As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
As $x \to \pm\infty$ , $f(x) \to -\infty$
$-9$
$4,\ -2$
It touches the x-axis and turns back
$x + 7$
$x^{2} + x + 1$
$33$
$19$
Yes, because $p(3) = 0$
$-4$
$4,\ 1,\ -1$
$x^{2} - 9$
1. Check that $p(2) = 0$ 2. Divide $p(x)$ by $x - 2$ 3. Solve the quadratic quotient $= 0$ 4. List $2$ with the solutions of the quadratic
$360$
$-4$
$31$
$4 - 4i$
None: two complex zeros
$4 + 3 i,\ 4 - 3 i$