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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