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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?
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 $x^2 + kx + 4$ ?
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 $1 + 2 + 4 + \dots + 2^{ 4 }$ .
$f(x) = \dfrac{ 4x + 6 }{x - 6}$ has a vertical asymptote $x = c$ . What is $c$ ?
$f(x) = \dfrac{ 5x + 6 }{ 2x + 4 }$ has a horizontal asymptote $y = k$ . What is $k$ ?
What is the horizontal asymptote of $f(x) = \dfrac{ 4x + 1}{x^2 + 6}$ ?
1. $y = 0$
2. $y = 4$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 8x + 1}{x^2 + 5}$ ?
1. $y = 0$
2. $y = 8$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 7x + 1}{x^2 + 6}$ ?
1. $y = 0$
2. $y = 7$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 8x + 1}{x^2 + 6}$ ?
1. $y = 0$
2. $y = 8$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 8x + 1}{x^2 + 1}$ ?
1. $y = 0$
2. $y = 8$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 5x + 1}{x^2 + 4}$ ?
1. $y = 0$
2. $y = 5$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 6x + 1}{x^2 + 2}$ ?
1. $y = 0$
2. $y = 6$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 8x + 1}{x^2 + 3}$ ?
1. $y = 0$
2. $y = 8$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 3x + 1}{x^2 + 1}$ ?
1. $y = 0$
2. $y = 3$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 6x + 1}{x^2 + 6}$ ?
1. $y = 0$
2. $y = 6$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 5x + 1}{x^2 + 6}$ ?
1. $y = 0$
2. $y = 5$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 4x + 1}{x^2 + 4}$ ?
1. $y = 0$
2. $y = 4$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 9x + 1}{x^2 + 9}$ ?
1. $y = 0$
2. $y = 9$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 3x + 1}{x^2 + 6}$ ?
1. $y = 0$
2. $y = 3$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 6x + 1}{x^2 + 3}$ ?
1. $y = 0$
2. $y = 6$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 7x + 1}{x^2 + 9}$ ?
1. $y = 0$
2. $y = 7$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 3x + 1}{x^2 + 4}$ ?
1. $y = 0$
2. $y = 3$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 4x + 1}{x^2 + 2}$ ?
1. $y = 0$
2. $y = 4$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 9x + 1}{x^2 + 4}$ ?
1. $y = 0$
2. $y = 9$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 3x + 1}{x^2 + 8}$ ?
1. $y = 0$
2. $y = 3$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 7x + 1}{x^2 + 7}$ ?
1. $y = 0$
2. $y = 7$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 5x + 1}{x^2 + 9}$ ?
1. $y = 0$
2. $y = 5$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 2x + 1}{x^2 + 6}$ ?
1. $y = 0$
2. $y = 2$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 6x + 1}{x^2 + 8}$ ?
1. $y = 0$
2. $y = 6$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 9x + 1}{x^2 + 1}$ ?
1. $y = 0$
2. $y = 9$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 9x + 1}{x^2 + 6}$ ?
1. $y = 0$
2. $y = 9$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 2x + 1}{x^2 + 3}$ ?
1. $y = 0$
2. $y = 2$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 2x + 1}{x^2 + 7}$ ?
1. $y = 0$
2. $y = 2$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 4x + 1}{x^2 + 1}$ ?
1. $y = 0$
2. $y = 4$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 5x + 1}{x^2 + 1}$ ?
1. $y = 0$
2. $y = 5$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 3x + 1}{x^2 + 2}$ ?
1. $y = 0$
2. $y = 3$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 3x + 1}{x^2 + 3}$ ?
1. $y = 0$
2. $y = 3$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 2x + 1}{x^2 + 9}$ ?
1. $y = 0$
2. $y = 2$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 2x + 1}{x^2 + 1}$ ?
1. $y = 0$
2. $y = 2$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 9x + 1}{x^2 + 2}$ ?
1. $y = 0$
2. $y = 9$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 6x + 1}{x^2 + 7}$ ?
1. $y = 0$
2. $y = 6$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 7x + 1}{x^2 + 4}$ ?
1. $y = 0$
2. $y = 7$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 6x + 1}{x^2 + 4}$ ?
1. $y = 0$
2. $y = 6$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 5x + 1}{x^2 + 8}$ ?
1. $y = 0$
2. $y = 5$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 8x + 1}{x^2 + 7}$ ?
1. $y = 0$
2. $y = 8$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 7x + 1}{x^2 + 5}$ ?
1. $y = 0$
2. $y = 7$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 6x + 1}{x^2 + 1}$ ?
1. $y = 0$
2. $y = 6$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 8x + 1}{x^2 + 8}$ ?
1. $y = 0$
2. $y = 8$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 7x + 1}{x^2 + 8}$ ?
1. $y = 0$
2. $y = 7$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 2x + 1}{x^2 + 8}$ ?
1. $y = 0$
2. $y = 2$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 3x + 1}{x^2 + 5}$ ?
1. $y = 0$
2. $y = 3$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 9x + 1}{x^2 + 7}$ ?
1. $y = 0$
2. $y = 9$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 9x + 1}{x^2 + 3}$ ?
1. $y = 0$
2. $y = 9$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 9x + 1}{x^2 + 5}$ ?
1. $y = 0$
2. $y = 9$
3. There is none, because the degrees are different
What is the horizontal asymptote of $f(x) = \dfrac{ 7x + 1}{x^2 + 2}$ ?
1. $y = 0$
2. $y = 7$
3. There is none, because the degrees are different
Where does the graph of $f(x) = \dfrac{x - 8}{x + 4}$ cross the $x$ -axis? Give $x$ .
$f(x) = \dfrac{(x - 5)(x + 6)}{x - 5}$ . At which $x$ does the graph have a hole?
$f(x) = \dfrac{(x - 1)(x + 3)}{x - 1}$ has a hole at $x = 1$ . What is the $y$ -coordinate of the hole?
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 $k$ ?
Simplify (x² − 4) ÷ (x − 2), that is, the fraction with numerator x² − 4 and denominator x − 2. Which answer is right?
1. x + 2, for x ≠ 2
2. x − 2
3. x + 2, for every x
Simplify (x² − 25) ÷ (x − 5), that is, the fraction with numerator x² − 25 and denominator x − 5. Which answer is right?
1. x + 5, for x ≠ 5
2. x − 5
3. x + 5, for every x
Simplify (x² − 9) ÷ (x − 3), that is, the fraction with numerator x² − 9 and denominator x − 3. Which answer is right?
1. x + 3, for x ≠ 3
2. x − 3
3. x + 3, for every x
Simplify (x² − 16) ÷ (x − 4), that is, the fraction with numerator x² − 16 and denominator x − 4. Which answer is right?
1. x + 4, for x ≠ 4
2. x − 4
3. x + 4, for every x
Simplify (x² − 36) ÷ (x − 6), that is, the fraction with numerator x² − 36 and denominator x − 6. Which answer is right?
1. x + 6, for x ≠ 6
2. x − 6
3. x + 6, for every x
Simplify (x² − 81) ÷ (x − 9), that is, the fraction with numerator x² − 81 and denominator x − 9. Which answer is right?
1. x + 9, for x ≠ 9
2. x − 9
3. x + 9, for every x
Simplify (x² − 64) ÷ (x − 8), that is, the fraction with numerator x² − 64 and denominator x − 8. Which answer is right?
1. x + 8, for x ≠ 8
2. x − 8
3. x + 8, for every x
Simplify (x² − 49) ÷ (x − 7), that is, the fraction with numerator x² − 49 and denominator x − 7. Which answer is right?
1. x + 7, for x ≠ 7
2. x − 7
3. x + 7, for every x
Multiply and simplify: (x + 8)/(x − 6) · (x − 6)/(x + 9).
Divide and simplify: x/(x + 3) ÷ x²/(x + 3).
Write 1/x + 1/(x + 8) as a single fraction.
Simplify 6/(x − 1) − 9/(x − 1).
What is the least common denominator of 1/(x² − 16) and 1/(x + 4)?
Solve $\dfrac{x}{x + 2} = \dfrac{ 2 }{ 7 }$ .
Solve $\dfrac{1}{x} + \dfrac{1}{ 11 } = \dfrac{1}{ 5 }$ .
Solve $\dfrac{x^2 - 4}{x - 2} = 4$ .
1. No solution: simplifying gives x = 2, but x = 2 makes the denominator 0
2. x = 2
3. Every x except 2
Solve $\dfrac{x^2 - 81}{x - 9} = 18$ .
1. No solution: simplifying gives x = 9, but x = 9 makes the denominator 0
2. x = 9
3. Every x except 9
Solve $\dfrac{x^2 - 9}{x - 3} = 6$ .
1. No solution: simplifying gives x = 3, but x = 3 makes the denominator 0
2. x = 3
3. Every x except 3
Solve $\dfrac{x^2 - 16}{x - 4} = 8$ .
1. No solution: simplifying gives x = 4, but x = 4 makes the denominator 0
2. x = 4
3. Every x except 4
Solve $\dfrac{x^2 - 49}{x - 7} = 14$ .
1. No solution: simplifying gives x = 7, but x = 7 makes the denominator 0
2. x = 7
3. Every x except 7
Solve $\dfrac{x^2 - 36}{x - 6} = 12$ .
1. No solution: simplifying gives x = 6, but x = 6 makes the denominator 0
2. x = 6
3. Every x except 6
Solve $\dfrac{x^2 - 64}{x - 8} = 16$ .
1. No solution: simplifying gives x = 8, but x = 8 makes the denominator 0
2. x = 8
3. Every x except 8
Solve $\dfrac{x^2 - 25}{x - 5} = 10$ .
1. No solution: simplifying gives x = 5, but x = 5 makes the denominator 0
2. x = 5
3. Every x except 5
Solve $\dfrac{x^2 - 1}{x - 1} = 2$ .
1. No solution: simplifying gives x = 1, but x = 1 makes the denominator 0
2. x = 1
3. Every x except 1

Answers

$15$
$54$
$10$
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 $p(3) = 0$
$-4$
$360$
$-4$
$31$
$6$
$\frac{5}{2}$
$y = 0$
$8$
$5$
$4$
$45$
$256$
$8$
x + 2, for x ≠ 2
$\frac{x + 8}{x + 9}$
$\frac{1}{x}$
$\frac{2 x + 8}{x \left(x + 8\right)}$
$- \frac{3}{x - 1}$
$x^{2} - 16$
$\frac{4}{5}$
$\frac{55}{6}$
No solution: simplifying gives x = 2, but x = 2 makes the denominator 0