Solve quadratic equations by factoring

About this lesson

Algebra I › Quadratic equations

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Solve quadratic equations by factoring

Warm-up

Three quick questions from earlier lessons.

Discover

To factor $x^2 + 7x + 10$ , you need two numbers that multiply to 10 and add to 7. Which?

2 and 5
1 and 10

Key idea

Factor, then use the zero product property.

x^2 + bx + c = (x + m)(x + n)

when

m \cdot n = c

and

m + n = b

. To solve by factoring: bring everything to one side, factor, set each factor to 0. A negative

c

means one number is negative.

Worked example

Solve $x^2 - 2x - 15 = 0$ .

(x - 5)(x + 3) = 0

−5 · 3 = −15, −5 + 3 = −2.

x = 5

or

x = -3

Zero product.

Your turn, guided

Your turn: $x^2 + 9x + 14 = (x + 2)(x + \;?)$ .

7

2 · 7 = 14.

Practice ★

$x^2 + 8x + 15 = (x + 3)(x + \;?)$
$x^2 + 17x + 72 = (x + 9)(x + \;?)$

Solve $x^2 - 9x + 14 = 0$ by factoring. Enter all solutions.

Watch out!

Practice ★★

Solve $x^2 + 8x - 9 = 0$ by factoring. Enter all solutions.
Solve $x^2 + 7x - 8 = 0$ by factoring. Enter all solutions.

Exit ticket

Three questions to check you have got it.

Solve $x^2 - 9x + 14 = 0$ by factoring. Enter all solutions.
Solve $x^2 - 17x + 72 = 0$ by factoring. Enter all solutions.
Solve $x^2 - 16x + 63 = 0$ by factoring. Enter all solutions.

Summary card

Solving by factoring

Multiply to $c$ , add to $b$ ; then each factor $= 0$ .

Watch out: the factor $x - 4$ gives $x = 4$ .

End of the lesson

Next lesson: Completing the square Back to the chapter

Answers: Solve quadratic equations by factoring

A

$5$
$8$

B

$7,\ 2$

C

$-9,\ 1$
$-8,\ 1$

D

$7,\ 2$
$8,\ 9$
$9,\ 7$

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