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Factoring Polynomials Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Greatest Common Factor The simplest method.

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Objectives The student will be able to: Factor using the greatest common factor (GCF). Algebra II – SHS 2012

Factoring Polynomials Factoring a polynomial means expressing it as the product of two or more polynomials. This means expressing it as polynomials multiplied by each other.

Review: What is the GCF of 25a2 and 15a? Let’s go one step further… 1) FACTOR 25a2 + 15a. Find the GCF and divide each term 25a2 + 15a = 5a( ___ + ___ ) Check your answer by distributing. 5a 3

2) Factor 18x2 - 12x3. Find the GCF 6x2 Divide each term by the GCF 18x2 - 12x3 = 6x2( ___ - ___ ) Check your answer by distributing. 3 2x

3) Factor 28a2b + 56abc2. GCF = 28ab Divide each term by the GCF 28a2b + 56abc2 = 28ab ( ___ + ___ ) Check your answer by distributing. 28ab(a + 2c2) a 2c2

Factor 20x2 - 24xy x(20 – 24y) 2x(10x – 12y) 4(5x2 – 6xy) 4x(5x – 6y)

5) Factor 28a2 + 21b - 35b2c2 GCF = 7 Divide each term by the GCF Check your answer by distributing. 7(4a2 + 3b – 5b2c2) 4a2 3b 5b2c2

Factor 16xy2 - 24y2z + 40y2 2y2(8x – 12z + 20) 4y2(4x – 6z + 10) 8xy2z(2 – 3 + 5)