General Advice for Factoring Polynomials By Patrica Hensley  Jefferson Davis Campus
Two terms 

Difference of Squares 
Sum of Cubes 
Difference of Cubes 
x^{2} – y^{2} = (x – y) (x + y) 
x^{3 }+ y^{3 }= (x + y)(x^{2 }– xy +y^{2}) 
x^{3} – y^{3} = (x – y) (x^{2} + xy +y^{2}) 
Ex. 4x^{2} – 9 = (2x – 3)(2x + 3) 
Ex. 8y^{3} + 27 = (2y + 3)(4y^{2 }– 6y + 9) 
Ex. 216x^{3} – 125 = (6x – 5)(36x^{2} + 30x +25) 
Three Terms 

Perfect Square Trinomial 
Trinomial 
x^{2} + 2xy + y^{2 }= (x + y)^{2} Ex. 36x^{2 }+ 60x +25 = (6x + 5)^{2} ^{} 
ax^{2} + bx + c Ex. 6k^{2} + 5kp – 6p^{2} = (3k – 2p)(2k + 3p) 
x^{2 }– 2xy + y^{2} = (x – y)^{2} Ex. x^{2} – 6x + 9 = (x – 3)^{2} 
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?