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Factoring Polynomials: Part 1

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.

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Factoring Polynomials: Part 1

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  1. 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, 16 15 = 3 • 5 16 = 2 • 2 • 2 • 2 GCF = 1 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 2) 72, 36, 42 72 = 2 • 2 • 2 • 3 • 3 36 = 2 • 2 • 3 • 3 42 = 2 • 3 • 7 GCF = 2 • 3 = 6

  2. Factoring a polynomial by its GREATEST COMMON FACTOR (GCF) “Reverse the Distributive Property” 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 1: 10x3z – 25x6y Step #1: GCF = 5x3 Step #2: Step #3: 5x3(2z – 5x3y) Exp 2: 14a3b2 + 28a5b5 + 35a2b4 Step #1: Step #2: Step #3:

  3. FACTORING PRACTICE #1: Factor by the GCF (1) 72a3 – 50ab2 (2) 6y5 + 30y4 + 24y3 (3) 10x2 – 45x + 35 (4) 2xy – 10x (5) 5x2y2 – 15x2y (6) 12x2 – 42xy + 9y2

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

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

  6. 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: (1st GCF + 2nd GCF) (factored polynomial) Algebraic Example Example: 10x2 + 5x + 6x + 3 GCF = 5x GCF = 3 5x(2x + 1) + 3(2x + 1) (5x+ 3) (2x + 1) a is first GCF and d is second GCF

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

  8. f) h) g) e)

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