1

Algebra 2: Section 5.2

Solving Quadratic Functions by Factoring

2

Factoring Quadratic Expressions

Factoring a Trinomial of the Form

When factoring ask yourself,

what two numbers multiply

together to be ‘c’ and add together

to be ‘b’.

2x bx c

3

21. 2 48x x

4

Factoring Quadratic Expressions

Factoring a Trinomial of the Form

First, look for common factor!

Trial and Error– Write down factors of a and c

– Try combinations until the correct factorization

is found

2ax bx c

5

22. 4y 4 3y

6

23. 10 19 7x x

7

24. 5 17 14x x

8

Factoring Quadratic Expressions

Difference of Two Squares

2 2 ( )( )a b a b a b

9

25. 49x 26. 16 225y

( 7)( 7)x x (4 15)(4 15)y y

10

Factoring Quadratic Expressions

Perfect Square Trinomial

2 2 2

2 2 2

2 ( )

2 ( )

a ab b a b

a ab b a b

11

27. 4 12 9z z 28. 36 60 25w w

2 2(2 ) 12 (3)z z

2 2(2 ) 2(2 )(3) (3)z z

2(2 3)z

2 2(6 ) 60 (5)w w

2 2(6 ) 2(6 )(5) (5)w w

2(6 5)w

12

General Steps for Factoring

Quadratic Expressions

1) If necessary, factor out any

common factor

2) Factor the new expression into

two binomials (if possible)

13

29. 14 2 12x x210. 3 18y y

211. 4 36x 212. 12 3 3x x

22(7 6)x x

2(7 6)( 1)x x

3 ( 6)y y

24( 9)x

4( 3)( 3)x x

23(4 1)x x

14

Solving Quadratic Equations

Zero Product Property

–If AB = 0, then A = 0 or B = 0

If ( 3)( 2) 0, thenx x

3 0 or 2 0x x

15

Solving Quadratic Equations

General Steps to Solve

–If necessary, move all terms to the

one side (leave zero on the other)

–If necessary, combine like terms

–Factor

–Solve using the Zero Product

Property

16

213. 9 12 4 0t t 214. 3 -6 10x x

2 2(3 ) 2(3 )( 2) ( 2) 0t t

2(3 2) 0t

3 2 0t

3 2t

2

3t

20 3 4x x

0 ( 4)( 1)x x

4 0 or 1 0x x

4 or 1x x

17

Finding Zeros of Quadratic

Functions

Zeros of a function

–The x-values at which the graph

crosses the x-axis

–when y = 0

18

215. 3 14 5y x x 216. 8 15y x x

20 3 14 5x x

0 (3 1)( 5)x x

3 1 0 or 5 0x x

3 1 or 5x x

1 or 5

3x x

20 8 15x x

0 ( 5)( 3)x x

5 0 or 3 0x x

5 or 3x x

Assignment

p.260

#23-87 odds, 92

(34 problems)

19

Assignment

p.260

#24-88 evens, 94

(34 problems)

Math Journal

Factoring with Algebra Tiles

p.262 #96 (parts a and b)20