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Factoring Review

Always Factor The Greatest Common Factor Out First!
Example: To factor 2x3 - 2x2 - 24x, first factor out 2x.

COMMON FORMS

a2 - b2 = (a + b)(a - b)

a4 - b4 = (a2 + b2)(a2 - b2) = (a2 + b2)(a + b)(a - b)

x2 + bx + c = (x + k1)(x + k2)  where k1 + k2 = b and k1● k2 = c.

ax2 + bx + c = (a1x + k1)(a2x + k2)  where a1● a2=a, k1● k2 = c,  and  a2k1 + a1k2 = b

Factoring By Grouping

AC + BC + DA + DB = C(A + B) + D(A  + B) = (C + D)(A + B)

Example:  2x2 + 9x + 10 =  2x2 + 4x + 5x + 10  =  2x(x + 2) + 5(x + 2) = (x + 2)(2x + 5)
The key here is to find two numbers that add to 9 but multiply out to 2x10 = 20. Those numbers are 4 and 5 so you rewrite 9x as 4x+5x.

There are nearly countless other forms of factorization, but these are the ones most commonly used.

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