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a\left(x^{2}+4x-12\right)
Factor out a.
p+q=4 pq=1\left(-12\right)=-12
Consider x^{2}+4x-12. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+px+qx-12. To find p and q, set up a system to be solved.
-1,12 -2,6 -3,4
Since pq is negative, p and q have the opposite signs. Since p+q is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -12.
-1+12=11 -2+6=4 -3+4=1
Calculate the sum for each pair.
p=-2 q=6
The solution is the pair that gives sum 4.
\left(x^{2}-2x\right)+\left(6x-12\right)
Rewrite x^{2}+4x-12 as \left(x^{2}-2x\right)+\left(6x-12\right).
x\left(x-2\right)+6\left(x-2\right)
Factor out x in the first and 6 in the second group.
\left(x-2\right)\left(x+6\right)
Factor out common term x-2 by using distributive property.
a\left(x-2\right)\left(x+6\right)
Rewrite the complete factored expression.