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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