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