Precalc0006to0010-page6 - coefficients That is the factors...

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(Section 0.7: Factoring Polynomials) 0.7.1 SECTION 0.7: FACTORING POLYNOMIALS LEARNING OBJECTIVES • Know techniques and formulas for factoring polynomials. • Know the Test for Factorability for factoring quadratic trinomials. • Recognize polynomials in quadratic form and be able to factor them. PART A: DISCUSSION • Factoring is a very commonly used technique in precalculus and calculus. Factoring helps us simplify expressions, find zeros, solve equations and inequalities, and find partial fraction decompositions (see Section 7.3). • Rewriting a sum of terms as a product of factors helps us perform sign analyses, as we will see in Sections 2.4 and 2.10. PART B: FACTORING OUT GCFs For now, when we factor a polynomial, we factor it completely over the integers ( ± ), meaning that the factors cannot be broken down further using only integer
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Unformatted text preview: coefficients. That is, the factors must be prime (or irreducible ) over the integers. • In Chapter 2, we will factor over other sets, such as ± , ± , or ± . TIP 1 : The Greatest Common Factor (GCF) , if it is not 1, should typically be factored out first, although it can be factored out piece-by-piece for more complicated expressions. (Unfortunately, there is no simple, standard definition for the GCF.) Example 1 (Factoring out a GCF) We factor 8 x + 6 as 2 4 x + 3 ( ) , because 2 is the GCF. 2 is the greatest common divisor of 8 and 6. § Example 2 (Factoring out a GCF) We factor x 5 + x 3 as x 3 x 2 + 1 ( ) , because x 3 is the GCF. x 3 is the power of x with the least exponent. §...
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This document was uploaded on 12/29/2011.

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