For all polynomials, first factor out the greatest common factor (GCF).
For a binomial, check to see if it is any of the following:
difference of squares: x 2 – y 2 = ( x + y) ( x – y)
difference of cubes: x 3 – y 3 = ( x – y) ( x 2 + xy + y 2)
sum of cubes: x 3 + y 3 = ( x + y) ( x 2 – xy + y 2)
For a trinomial, check to see whether it is either of the following forms:
x 2 + bx + c:
If so, find two integers whose product is c and whose sum is b. For example,
x 2 + 8 x + 12 = ( x + 2)( x + 6)
since (2)(6) = 12 and 2 + 6 = 8
ax 2 + bx + c:
If so, find two binomials so that
the product of first terms = ax 2
the product of last terms = c
the sum of outer and inner products = bx
See the following polynomial in which the product of the first terms = (3 x)(2 x) = 6 x 2, the product of last terms = (2)(–5) = –10, and the sum of outer and inner products = (3 x)(–5) + 2(2 x) = –11 x.
For polynomials with four or more terms, regroup, factor each group, and then find a pattern as in steps 1 through 3.
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