Transcript Chapter 7 Section 1 - Shelton State Community College

Greatest Common Factors;
Factoring by Grouping
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Sec 7.1 - 1
Factoring Out the Greatest Common Factor
The first step in factoring is to find the greatest common
factor (GCF) – the largest term that divides each term of the
polynomial. The GCD is a factor of all the terms of the
polynomial.
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Factoring Out the Greatest Common Factor
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Factoring Out a Binomial Factor
The greatest common factor need not be a monomial.
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Factoring Out a Negative Common Factor
When the coefficient of the term of greatest degree is
negative, it is sometimes preferable to factor out the –1 that is
understood along with the GCF.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
7.1 Greatest Common Factors; Factoring by Grouping
Factoring by Grouping
Many polynomials have no greatest common factor other
than the number 1. Some of these can be factored using the
distributive property if those terms with a common factor are
grouped together. Consider the polynomial:
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Sec 7.1 - 6
Factoring by Grouping
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Copyright © 2010 Pearson Education, Inc. All rights reserved.
Factoring by Grouping
Copyright © 2010 Pearson Education, Inc. All rights reserved.
Sec 7.1 - 8
Factoring by Grouping
Copyright © 2010 Pearson Education, Inc. All rights reserved.