Factoring Special Polynomials MTH 100 Factoring Special Polynomials

Overview Special polynomials fall into three broad categories:

1. Difference of Squares a2 – b2 = (a + b)(a – b) Both terms are perfect squares. There is a subtraction sign between the terms.

2. Sum/Difference of Cubes a3 + b3 = (a + b)(a2 – ab + b2) a3 – b3 = (a – b)(a2 + ab + b2) Both terms are perfect cubes. Pay close attention to the factor patterns, and watch your signs. The trinomial in the pattern does not factor again.

Examples

3. Perfect Square Trinomials a2 – 2ab + b2 = (a – b)(a – b) = (a – b)2 a2 + 2ab + b2 = (a + b)(a + b) = (a + b)2 The first and last terms are perfect squares. The last sign is positive. The middle term is two times the square root of the first and last terms.

Examples

4. And if by chance they are not special… Look for a GCF Count the terms: Two terms? Check for difference of squares or sum/difference of cubes. Three terms? Check for perfect square trinomial. If not, guess-and-check or AC. Four terms? Try factor by grouping.

Examples