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Introduction to Factoring
5.1 Factoring Monomials Factoring When Terms Have a Common Factor Factoring by Grouping Checking by Evaluating
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Factoring To factor a polynomial is to find an equivalent expression that is a product. An equivalent expression of this type is called a factorization of the polynomial.
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Find three factorizations of 24x3
Find three factorizations of 24x3. Solution a) 24x3 = b) 24x3 = c) 24x3 =
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Factoring When Terms Have a Common Factor
To factor a polynomial with two or more terms of the form ab + ac, we use the distributive law with the sides of the equation switched: ab + ac = a(b + c). Multiply Factor 4x(x2 + 3x 4) 4x3 + 12x2 16x
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Factor: 9a 21. Solution
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Sage and Scribe Factor: 9a3b4 + 18a2b3 Solution Factor: 28x6 + 32x3. Solution
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Factor: 12x5 21x4 + 24x3 Solution
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Factor: 4xy + 8xw 12x Solution
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Tips for Factoring 1. Factor out the largest common factor, if one exists. 2. The common factor multiplies a polynomial with the same number of terms as the original polynomial. 3. Factoring can always be checked by multiplying. Multiplication should yield the original polynomial.
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Factor x2(x + 2) + 3(x + 2). Solution
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If a polynomial can be split into groups of terms and the groups share a common factor, then the original polynomial can be factored. This method, known as factoring by grouping, can be tried on any polynomial with four or more terms.
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Sage and Scribe Factor by grouping. a) 3x3 + 9x2 + x + 3
b) 9x4 + 6x 27x3 18
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