Factoring Polynomials: Part 1GREATEST COMMON FACTOR (GCF) is the product of all prime factors that are shared by all terms and the smallest exponent of any variable common to all terms.

•LARGEST NUMBER that can divide all terms

•SMALLEST EXPONENT of common variables to all terms

Examples:1) 15, 1615 = 3 • 516 = 2 • 2 • 2 • 2

GCF = 1

2) 72, 36, 42

72 = 2 • 2 • 2 • 3 • 3

36 = 2 • 2 • 3 • 3

42 = 2 • 3 • 7

GCF = 2 • 3 = 6

3) 6x2y6, 32x3y4, 10x5y3

6x2y6 = 2 • 3 • x2 • y6

32x3y4 = 2 • 2 • 2 • 2 • x3 • y4

10x5y3= 2• 5 • x5 • y3

GCF = 2 • x2 • y3 = 2x2y3

Factoring a polynomial by its GREATEST COMMON FACTOR (GCF)

“Reverse the Distributive Property”

Exp 1: 10x3z – 25x6y

Step #1: GCF = 5x3

Step #2:

Step #3: 5x3(2z – 5x3y)

STEP #1: Find the GCF for all terms of polynomial

STEP #2: Find Factored Polynomial by dividing all terms by GCF

STEP #3: Factored Form = (Step #1)(Step #2)

yxzx

yx

x

zx 33

6

3

3

525

25

5

10

Exp 2: 14a3b2 + 28a5b5 + 35a2b4

Step #1:

Step #2:

Step #3:

FACTORING PRACTICE #1: Factor by the GCF

(5) 5x2y2 – 15x2y (6) 12x2 – 42xy + 9y2

(1) 72a3 – 50ab2 (2) 6y5 + 30y4 + 24y3

(3) 10x2 – 45x + 35 (4) 2xy – 10x

Factoring Polynomials: Part 2

))((22 bababa [1] Difference of Squares

MEMORIZE!!!

Special Binomial (2 Term) Factoring Techniques

EXP#1: 162 x EXP#2: 22 yx

EXP#3: 964 2 xxxx 2 4416

)4)(4( xx

FACTORING PRACTICE #2: Difference of Squares

a) 94 2 x b) 19 2 x

c) 2216 yx d) 2925 x

e) 6481 4 y f) 24 100xx

))((

)()(

cbda

cbdcba

dcbdacab

Factoring Polynomials: Part 34 – Term Polynomials

STEP #1: Check for GCF of entire polynomial

STEP #2: Factor by Grouping

•Split polynomial: FIRST two terms and the LAST two terms.

•FACTOR the GCF from both sides of split

•Check for negative and positive sign agreement

•Factored Form: (1st GCF + 2nd GCF) (factored polynomial)

Algebraic Example

a is first GCF and d is second GCF

Example: 10x2 + 5x + 6x + 3

5x(2x + 1) + 3(2x + 1)

GCF = 5x GCF = 3

(5x+ 3) (2x + 1)

FACTORING PRACTICE #5: Factoring by Grouping

a) 10 - 5n - 24m + 12mn b) y + xy - x - 321535

c) mnnmmn 22 248 d) 22 3515 yxyxyx

e) 22 44 yxyxyx f) mnnmmn 2233

g) xxxx 612510 223 h) 22 211496 yxyxyx