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For all polynomials, first factor out the greatest common factor (GCF).
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For a binomial, check to see if it is any of the following:
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difference of squares: x2 − y2 = ( x + y) ( x − y)
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difference of cubes: x3 − y3 = ( x − y) ( x2 + xy + y2)
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sum of cubes: x3 + y3 = ( x + y) ( x2 − xy + y2)
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For a trinomial, check to see if it is either of the following forms:
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x2 + bx + c:
If so, find two integers whose product is c and whose sum is b. For example,
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ax2 + bx + c:
If so, find two binomials so that
the product of first terms = ax2
the product of last terms = c
the sum of outer and inner products = bx
See the following where the product of first terms = (3 x)(2 x) = 6 x2, the product of last terms = (2)(−5) = −10, and the sum of outer and inner products = (3 x)(−5) + 2(2 x) = −11 x.
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For polynomials with four or more terms, regroup, factor each group, and then find a pattern as in Steps 1 through 3.












Linear Sentences in One Variable
Factoring Polynomials