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Wednesday, October 16, 2002 Factoring the GCF from Polynomials

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Wednesday, October 16, 2002 Review Algebraic Factorization is the writing of an expression as the product of prime numbers and variables with no variables having an exponent greater than one.

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Wednesday, October 16, 2002 Example: 14x 2 y = 2 7 x x y

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Wednesday, October 16, 2002 Steps for Factoring the GCF From Polynomials 1.Write down the problem.

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Wednesday, October 16, 2002 Steps for Factoring the GCF From Polynomials 2.Write each term on a separate line and then write the algebraic factorization of each term.

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Wednesday, October 16, 2002 Steps for Factoring the GCF From Polynomials 3.Pair up all factors that occur in each term and circle them.

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Wednesday, October 16, 2002 Steps for Factoring the GCF From Polynomials 4.Multiply what is circled. This is the GCF. When writing the answer, put it outside parenthesis. The left- overs for each term should be multiplied and put inside parenthesis.

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Wednesday, October 16, 2002 Example Step 1 Step 2 3x 3 + 6x 2 y – 15xy 2 3x 3 = 3 x x x 6x 2 y= 2 3 x x y 15xy 2 = 3 5 x y y

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Wednesday, October 16, 2002 Example Step 3 Example Step 3 Step 4 3x 3 = 3 x x x 6x 2 y= 2 3 x x y 15xy 2 = 3 5 x y y 3x (x 2 + 2xy – 5y 2 )

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Wednesday, October 16, 2002 Examples We will do these together on the board. A.12a 2 b + 90a 2 b 2 c B.32m 2 n 3 – 8m 2 n + 56m 3 n 2

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Wednesday, October 16, 2002 Try these yourself. 1.15x 2 – 20xy 2.3x 2 + 15x 3.20abc + 15a 2 c – 5ac

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5 Minute Check Simplify each expression. Complete in your notes. 1. (-3x - 2) - (7x + 9) 2. (-2x - 1) - (x - 7) 3. (9x + 5) - (6x - 8) 4. (-8x + 1) - (8x.

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