Algebra II

For all polynomials, first factor out the greatest common factor (GCF).

For a binomial, check to see if it is any of the following:

1. difference of squares: x ² – y ² = ( x + y) ( x – y)

2. difference of cubes: x ³ – y ³ = ( x – y) ( x ² + xy + y ²)

3. 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:

1. 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

2. 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.

   

3. 

For polynomials with four or more terms, regroup, factor each group, and then find a pattern as in steps 1 through 3.