algebra 2: section 6.4

Algebra 2: Section 6.4

Factoring and Solving Polynomial Equations

Factoring Quadratics

1. 4x2 24x

4x(x 6)

Common Factor: 4x

Factoring Quadratics

2. 2x2 11x 21

(2x_____)(x_____)

Two factors of -21 that when

FOI LED make the middle

term +11

(2x 3)(x 7)

Factoring Quadratics

23. 4x 36 81x

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

(2x 9)2

Perfect Square Trinomial

Sum and Difference of Cubes

a3 b3 (a b)(a2 ab b2)

a3 b3 (a b)(a2 ab b2)

x3 64 (x 4)(x2 4x 16)

27x3 8 (3x 2)(9x2 6x 4)

Examples

4. 125 x3

x3 53

(x 5)(x2 5x 52)

(x 5)(x2 5x 25)

Rewrite as sum of cubes

(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’

Examples

5. x2y2 3x2 4y2 12

x2(y2 3) 4(y2 3)

(y2 3)(x2 4)

(y2 3)(x 2)(x 2)

Difference of two squares

Examples2 2 3 46. a 8 16b ab b

b2(a2 8ab 16b2)

b2(a 4b)(a 4b)

b2(a 4b)2

Examples47. 25x 36

(5x2)2 (6)2

Difference of two squares

(5x2 6)(5x2 6)

W hich method of factoring?

• 2 terms

• 3 terms

• 4 terms

• Diff. of Squares

• Sum or Diff. of Cubes

• Trial and Error

• Perfect Square Trinomial

• Grouping

Always look for common

factor!!

Solving Polynomial Equations by

Factoring

(Examples)58. 2 18 0y y

42 ( 9) 0y y2 22 ( 3)( 3) 0y y y

Difference of two squares

2 22 0 3 0 3 0y or y or y

0 3 3y or y or y i

0 3y or yFor this assignment,

only concerned with

real solut ions

More Examples5 29. 4 108 0x x

2 34 ( 27) 0x x2 24 ( 3)( 3 9) 0x x x x

Difference of two cubes

2 24 0 3 0 3 9 0x or x or x x

3 9 4(1)(9)0 3

2x or x or x

0 3x or xThis is going to be

imaginary.

The discriminant is

negative!

Assignment

• p.349

# 33-85 all, 87, 88

(55 problems)

• Due W ednesday!