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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. x 121 2 25 x 144 2 2 x 72 2 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 8b g 3 3 x 343 3 8m 216n 3 3 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 x 2x 1 2 49 y 56 y 16 2 y 8 y 16 6 3 4. And if by chance they are not special… 1. Look for a GCF 2. Count the terms: a) Two terms? Check for difference of squares or sum/difference of cubes. b) Three terms? Check for perfect square trinomial. If not, guess-and-check or AC. c) Four terms? Try factor by grouping. Examples 15b 95b 70 2 24 y 10 y 6 y 3 2 y 54 y 6 2 3