0.5_bzca5e - Section P5 Factoring Polynomials Common...

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Section P5 Factoring Polynomials
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Common Factors
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Factoring a polynomial containing the sum of monomials mean finding an equivalent expression that is a product. In this section we will be factoring over the set of integers, meaning that the coefficients in the factors are integers. Polynomials that cannot be factored using integer coefficients are called prime.
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Example Factor: 2 3 2 64 28 5 ( 1) 10 ( 1) x x xy z xy z - - + -
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Factoring by Grouping
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Sometimes all of the terms of a polynomial may not contain a common factor. However, by a suitable grouping of terms it may be possible to factor. This is called factoring by grouping.
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Example Factor by Grouping: 3 2 4 5 20 x x x + - -
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Example Factor by Grouping: 3 2 2 8 7 28 x x x - + -
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Factoring Trinomials
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Factors of 8 8,1 4,2 -8,-1 -4,-2 Sum of Factors 9 6 -9 -6 Factor: 2 6 8 x x + + ( 29 ( 29 x x 4 2 + + Choose either two positive or two negative factors since the sign in front of the 8 is positive.
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Factor: 2 2 9 5 x x + - ( 29 ( 29 2 x x + - Possible factorizations
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0.5_bzca5e - Section P5 Factoring Polynomials Common...

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