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General Advice for Factoring Polynomials By Patrica Hensley - Jefferson Davis Campus

1. Always factor out the greatest common factor first.
2. If the polynomial to be factored is a binomial, then it may be a difference of two squares or a sum or difference of two cubes (remember that a sum of two squares does not factor).

3.  Two terms Difference of Squares Sum of Cubes Difference of Cubes x2 ñ y2 = (x ñ y) (x + y) x3 + y3 = (x + y)(x2 ñ xy +y2) x3 ñ y3 = (x ñ y) (x2 + xy +y2) Ex. 4x2 ñ 9 = (2x ñ 3)(2x + 3) Ex. 8y3 + 27 = (2y + 3)(4y2 ñ 6y + 9) Ex. 216x3 ñ 125 = (6x ñ 5)(36x2 + 30x +25)

4. If the polynomial to be factored is a trinomial, then
1. If two of the three terms are perfect squares, the polynomial may be a perfect square.
2. Otherwise, the polynomial may be one of the general forms.

 Three Terms Perfect Square Trinomial Trinomial x2 + 2xy + y2 = (x + y)2 Ex. 36x2 + 60x +25 = (6x + 5)2 ax2 + bx + c Ex. 6k2 + 5kp ñ 6p2 = (3k ñ 2p)(2k + 3p) x2 ñ 2xy + y2 = (x ñ y)2 Ex. x2 ñ 6x + 9 = (x ñ 3)2

5. If the polynomial to be factored consists of four or more terms, then try factoring by grouping.
6.  Four Terms May factor by grouping Ex. 10ab ñ 6b + 35a ñ 21 = 2b(5a ñ 3) + 7(5a ñ 3) = (5a ñ 3) (2b + 7)

5. Can any factors be factored further?