Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Example 1A

Solve the equation. Check your answer.

(x – 7)(x + 2) = 0

x – 7 = 0 or x + 2 = 0

x = 7 or x = –2

The solutions are 7 and –2.

Set each factor = 0

Solve each equation.

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Example 1A Continued

Substitute each solution for x into the original equation.

Check (x – 7)(x + 2) = 0

(7 – 7)(7 + 2) 0(0)(9) 0

0 0Check (x – 7)(x + 2) = 0

(–2 – 7)(–2 + 2) 0(–9)(0) 0

0 0

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Example 1B

Solve each equation. Check your answer.

x(x – 2) = 0

x = 0 or x – 2 = 0x = 2

The solutions are 0 and 2.

Set each factor = 0

Solve the second equation.

Substitute each solution for x into

the original equation.

Check (x – 2)(x) = 0

(0 – 2)(0) 0

(–2)(0) 00 0

(x – 2)(x) = 0

(2 – 2)(2) 0 (0)(2) 0

0 0

x(x – 2) = 0

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Solve each equation. Check your answer.

Check It Out! Example 1a

x(x + 4) = 0

x = 0 or x + 4 = 0x = –4

The solutions are 0 and –4.

Set each factor = 0

Solve the second equation.

Substitute each solution for x into

the original equation.

Check (x)(x + 4) = 0

(0)(0 + 4) 0

(0)(4) 0 0 0

(x)(x +4) = 0

(–4)(–4 + 4) 0(–4)(0) 0

0 0

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Check It Out! Example 1b

Solve the equation. Check your answer.

(3x + 4)(5x – 3) = 0

3x + 4 = 0 or 5x – 3 = 0 Set each factor = 0

Solve each equation.

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

If a quadratic equation is written in standard form, ax2 + bx + c = 0, then to solve the equation, you may need to factor before using the Zero Product Property.

Holt Algebra 2

5-3 Solving Quadratic Equations by Graphing and Factoring

Find the zeros of the function by factoring.

Example 2A: Finding Zeros by Factoring

f(x) = x2 – 4x – 12

x2 – 4x – 12 = 0

(x + 2)(x – 6) = 0

x + 2 = 0 or x – 6 = 0

x= –2 or x = 6

Set the function equal to 0.

Factor: Find factors of –12 that add to –4.

Set factors = 0

Solve each equation.

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Example 2A: Solving Quadratic Equations by Factoring

Solve the quadratic equation by factoring. Check your answer.

x2 – 6x + 8 = 0

(x – 4)(x – 2) = 0

x – 4 = 0 or x – 2 = 0

x = 4 or x = 2The solutions are 4 and 2.

Factor the trinomial.

Set each factor = 0

Solve each equation.

x2 – 6x + 8 = 0

(4)2 – 6(4) + 8 016 – 24 + 8 0

0 0

Checkx2 – 6x + 8 = 0

(2)2 – 6(2) + 8 0 4 – 12 + 8 0

0 0

Check

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Example 2C: Solving Quadratic Equations by Factoring

Solve the quadratic equation by factoring. Check your answer.

x2 – 12x + 36 = 0

(x – 6)(x – 6) = 0

x – 6 = 0 or x – 6 = 0

x = 6 or x = 6

Both factors result in the same solution, so there is one solution, 6.

Factor the trinomial.

Solve each equation.

Holt Algebra 2

5-3 Solving Quadratic Equations by Graphing and Factoring

Check It Out! Example 2a

f(x)= x2 – 5x – 6

Find the zeros of the function by factoring.

x2 – 5x – 6 = 0

(x + 1)(x – 6) = 0

x + 1 = 0 or x – 6 = 0

x = –1 or x = 6

Set the function equal to 0.

Factor: Find factors of –6 that add to –5.

Solve each equation.

Holt Algebra 2

5-3 Solving Quadratic Equations by Graphing and Factoring

Check It Out! Example 2b

g(x) = x2 – 8x

Find the zeros of the function by factoring.

x2 – 8x = 0

x(x – 8) = 0

x = 0 or x – 8 = 0

x = 0 or x = 8

Set the function to equal to 0.

Factor: Need factors of 0 that add to -8

Solve each equation.

Holt Algebra 2

5-3 Solving Quadratic Equations by Graphing and Factoring

Find the zeros of the function by factoring.

Example 2B: Finding Zeros by Factoring

g(x) = 3x2 + 18x

3x2 + 18x = 0

3x = 0 or x + 6 = 0

x = 0 or x = –6

Set the function to equal to 0.

Factor: Divide by 3,

then find factors of 0 that add to 6

Solve each equation.

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Check It Out! Example 2a Solve the quadratic equation by factoring. Check your answer.

x2 – 6x + 9 = 0

(x – 3)(x – 3) = 0

x – 3 = 0 or x – 3 = 0

x = 3 or x = 3Both equations result in the same solution, so there is one solution, 3.

Factor the trinomial.

Solve each equation.

x2 – 6x + 9 = 0

(3)2 – 6(3) + 9 09 – 18 + 9 0

0 0

Check

Substitute 3 into the original equation.

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Check It Out! Example 2d

Solve the quadratic equation by factoring. Check your answer.

3x2 – 4x + 1 = 0

(3x – 1)(x – 1) = 0

or x = 1

Factor the trinomial.

Solve each equation.

3x – 1 = 0 or x – 1 = 0

The solutions are and x = 1.

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Lesson Quiz: Part I

Solve each equation. Check your answers.

1. (x – 10)(x + 5) = 0

2. (x + 5)(x) = 0

Solve each quadratic equation by factoring. Check your answer.

3. x2 + 16x + 48 = 0•

10, –5

–5, 0

–4, –12

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Lesson Quiz: Part II

1, –7

–9

5. 2x2 + 12x – 14 = 0

6. x2 + 18x + 81 = 0