Algebra 2: Section 6.4

Factoring and Solving Polynomial Equations

(Day 1)

Review of Factoring• Factor out GCF if

present

• Decide on what type of factoring based on the # of terms

• 2 Terms:– Difference of Squares– Difference or Sum of Cubes

• 3 Terms:– Trial and Error– Perfect Square Trinomial

• 4 Terms:– Grouping

Factoring Quadratics

1. 4x 2 24x

4x(x 6)

Common Factor: 4xCommon Factor: 4x

Factoring Quadratics

2. 2x2 11x 21

(2x _____)(x _____)

Two # that Two # that multiply to get -multiply to get -

21 and add up 21 and add up when foiled to when foiled to

get +11get +11

(2x 3)(x 7)

Factoring Quadratics23. 4x 36 81x

(2x)2 22x 9 (9)2

(2x 9)2

Perfect Square TrinomialPerfect Square Trinomial2 22a ab b

2( )a b

Sum and Difference of Cubes

a3 b3 (a b)(a2 ab b2)

a3 b3 (a b)(a2 ab b2)

34. 64x 2( 4)( 4 16)x x x

35. 27 8x 2(3 2)(9 6 4)x x x

Examples36. 125 x

x 3 53

(x 5)(x 2 5x 52)

(x 5)(x 2 5x 25)

Rewrite as sum of cubesRewrite as sum of cubes(Changed order, standard)(Changed order, standard)

Factoring by Grouping(used when there are 4 terms)

• Factor common factor out of first two terms and factor another common factor out of last two terms(may need to rearrange)

• Factor common binomial out of each ‘term’

Examples2 2 2 27. x 3 4 12y x y

(y 2 3)(x 2 4)

(y 2 3)(x 2)(x 2)

Difference of two squaresDifference of two squares

Parentheses Parentheses should be the should be the

same!same!2 2x ( 3)y 24( 3)y

Examples2 2 3 48. a 8 16b ab b

b2(a2 8ab16b2)

b2(a 4b)(a 4b)

b2(a 4b)2

Examples49. 25x 36

(5x 2)2 (6)2

Difference of two squaresDifference of two squares

(5x 2 6)(5x 2 6)

Homework

• P.349#34-58 evens