Factoring Review
Always Factor The Greatest Common Factor Out First!
Example: To factor 2x^{3}  2x^{2}  24x, first factor
out 2x.
COMMON FORMS
a^{2}  b^{2} = (a + b)(a  b)
a^{4}  b^{4} = (a^{2} + b^{2})(a^{2}
 b^{2}) = (a^{2} + b^{2})(a + b)(a  b)
x^{2} + bx + c = (x + k_{1})(x + k_{2})
where k_{1} + k_{2} = b and k_{1}● k_{2}
= c.
ax^{2} + bx + c = (a_{1}x + k_{1})(a_{2}x
+ k_{2}) where a_{1}● a_{2}=a, k_{1}●
k_{2} = c, and a_{2}k_{1} +
a_{1}k_{2} = b
Factoring By Grouping
AC + BC + DA + DB = C(A + B) + D(A + B) = (C + D)(A + B)
Example: 2x^{2} + 9x + 10 = 2x^{2} + 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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