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7-2 Factoring by GCF Classwork: 01/23/17 Simplify. 1. 2(w + 1) 2. 3x(x2 – 4) Find the GCF of each pair of monomials. 3. 4h2 and 6h Holt McDougal Algebra 1 7-2 Factoring by GCF Essential Questions How do you factor polynomials by using the greatest common factor? Holt McDougal Algebra 1 7-2 Factoring by GCF Writing Math Aligning common factors can help you find the greatest common factor of two or more terms. Holt McDougal Algebra 1 7-2 Factoring by GCF Example 1A: Factoring by Using the GCF Factor each polynomial. Check your answer. 2x2 – 4 2x2 = 2 xx 4=22 Find the GCF. 2 2x2 – (2 2) The GCF of 2x2 and 4 is 2. 2(x2 – 2) Check 2(x2 – 2) 2x2 – 4 Holt McDougal Algebra 1 The product is the original polynomial. 7-2 Factoring by GCF Example: Factoring by Using the GCF 8x3 – 4x2 – 16x 8x3 = 2 2 2 x x x Find the GCF. 4x2 = 2 2 xx 16x = 2 2 2 2 x The GCF of 8x3, 4x2, and 16x is 4x. 22 x = 4x 4x(2x2 – x – 4) Check 4x(2x2 – x – 4) 8x3 – 4x2 – 16x Holt McDougal Algebra 1 The product is the original polynomials. 7-2 Factoring by GCF Example: Factoring by Using the GCF 3x3 + 2x2 – 10 3x3 = 3 2x2 = 2 x x x Find the GCF. xx 10 = 2 5 There are no common factors other than 1. 3x3 + 2x2 – 10 Holt McDougal Algebra 1 The polynomial cannot be factored further. 7-2 Factoring by GCF Example: Factoring Out a Common Binomial Factor A. 5(x + 2) + 3x(x + 2) (x + 2)(5 + 3x) Factor out (x + 2). B. –2b(b2 + 1)+ (b2 + 1) (b2 + 1)(–2b + 1) Holt McDougal Algebra 1 Factor out (b2 + 1). 7-2 Factoring by GCF Example: Factoring Out a Common Binomial Factor Factor each expression. C. 4z(z2 – 7) + 9(2z3 + 1) There are no common – 7) + + 1) factors. The expression cannot be factored. Leave it the same way as the final answer 4z(z2 Holt McDougal Algebra 1 9(2z3 7-2 Factoring by GCF You may be able to factor a polynomial by grouping. When a polynomial has four terms, you can make two groups and factor out the GCF from each group. Holt McDougal Algebra 1 7-2 Factoring by GCF Example: Factoring by Grouping 6h4 – 4h3 + 12h – 8 (6h4 – 4h3) + (12h – 8) Group terms that have a common number or variable as a factor. 2h3(3h – 2) + 4(3h – 2) (3h – 2)(2h3 + 4) Factor out (3h – 2). Check (3h – 2)(2h3 + 4) = Holt McDougal Algebra 1 6h4 – 4h3 + 12h – 8 7-2 Factoring by GCF Lesson Quiz: Factor each polynomial. (byb GCF) 1. 16x + 20x3 2. 4m4 – 12m2 + 8m Factor each expression. (by grouping) 3. 7k(k – 3) + 4(k – 3) 4. 3y(2y + 3) – 5(2y + 3) Holt McDougal Algebra 1