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Polynomial Factoring Explained: Common Techniques and Examples

Learn how to factor polynomials using the Greatest Common Factor (GCF) method and special binomial techniques. Step-by-step instructions and examples provided for easy understanding.

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Polynomial Factoring Explained: Common Techniques and Examples

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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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