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).
   




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




3. 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 – 6p2 = (3k – 2p)(2k + 3p)
x2 – 2xy + y2 = (x – y)2 Ex. x2 – 6x + 9 = (x – 3)2




4. If the polynomial to be factored consists of four or more terms, then try factoring by grouping.

Four Terms

May factor by grouping

Ex. 10ab – 6b + 35a – 21 = 2b(5a – 3) + 7(5a – 3) = (5a – 3) (2b + 7)

 

5. Can any factors be factored further?