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

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Presentation transcript:

Factoring Polynomials: Part 1 GREATEST 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, = = GCF = 1 2) 72, 36, = = = GCF = 2 3 = 6 3) 6x 2 y 6, 32x 3 y 4, 10x 5 y 3 6x 2 y 6 = 2 3 x 2 y 6 32x 3 y 4 = x 3 y 4 10x 5 y 3 = 2 5 x 5 y 3 GCF = 2 x 2 y 3 = 2x 2 y 3

Find the GREATEST COMMON FACTOR (GCF) for each of the following group of terms (1) 45, 75 (4) 36x 2 y, 54xy 2 z (7) 27xy, 18x, 12x 2 (2) 14, 49 (5) 45a 5 b 3, 60a 2 b 7 (8) 144a 2 b 2, 36ab 2, 12ab (3) 36, 90, 42 (6) 4pq 3, 15qr 2 (9) 25r 3 s 6 t 2, 15r 5 s 2 t 3, 75r 4 s 3 t

Factoring a polynomial by GREATEST COMMON FACTOR (GCF) “Reverse the Distributive Property” Exp 1: 10x 3 z – 25x 6 y Step #1: GCF = 5x 3 Step #2: Step #3: 5x 3 (2z – 5x 3 y) 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) Exp 2: 14a 3 b a 5 b a 2 b 4 Step #1: Step #2: Step #3:

FACTORING PRACTICE #1: Factor by the GCF (5) 5x 2 y 2 – 15x 2 y (6) 12x 2 – 42xy + 9y 2 (1) 72a 3 – 50ab 2 (2) 6y y y 3 (3) 10x 2 – 45x + 35(4) 2xy – 10x

Factoring Polynomials: Part 2 [1] Difference of Squares MEMORIZE!! Special Binomial (2 Term) Factoring Techniques EXP#1: EXP#2: EXP#3:

FACTORING PRACTICE #2: Difference of Squares a) b) c) d) e) f)

[2] Sum and Difference of Cubes MEMORIZE! EXP#1: EXP#2: MEMORIZE!

FACTORING PRACTICE #3: Sum and Difference of Cubes a) b) c) d) e) f)

FACTORING PRACTICE #4: Check for GCF, then 2 Term Cases a) b) c) d) e) f)

Factoring Polynomials: Part 3 4 – 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: (1 st GCF + 2 nd GCF) (factored polynomial) Algebraic Example a is first GCF and d is second GCF Example: 10x 2 + 5x + 6x + 3 5x(2x + 1) + 3(2x + 1) GCF = 5x GCF = 3 (5x+ 3) (2x + 1)

FACTORING PRACTICE #5: Factoring by Grouping a) b) c) d)

e)f) g) h)