Factoring Polynomials

I have included the most common formulas for factoring polynomials in this list.

Factoring out the Greatest Common Factor

bulletca + cb = c(a + b)
bulletca - cb = c(a - b)

Difference of Squares

bulleta2 - b2 = (a + b)(a - b)

Sum of Squares

bulleta2 + b2  This is a prime polynomial and can NOT be factored.

Perfect Square Trinomials

bulleta2 + 2ab + b2 = (a + b)(a + b) = (a + b)2
bulleta2 - 2ab + b2 = (a - b)(a - b) = (a - b)2

Other Common Polynomials

bulleta2 + (c + d)a + cd = (a +c)(a + d)
bulleta3 + 3a2b + 3ab2 + b3 = (a + b)3
bulleta3 - 3a2b + 3ab2 - b3 = (a - b)3
bulleta4 - 4a3b + 6a2b2 + 4ab3 - b4 = (a - b)4
bulleta3 - b3 = (a - b)(a2 + ab + b2)
bulleta3 + b3 = (a + b)(a2 - ab + b2)