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Factor. $\newline$ $8v^2 - 64v + 96$

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Factor quadratics

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Q. Factor.

\newline

8v^2 - 64v + 96

Identify GCF: Identify the greatest common factor (GCF) of the terms. $\newline$ GCF of $8v^2$ , $-64v$ , and $96$ is $8$ .
Factor out GCF: Factor out the GCF from the quadratic expression. $8(v^2 - 8v + 12)$
Find two numbers: Look for two numbers that multiply to give $ac$ (product of $a$ and $c$ in $av^2 + bv + c$ ) and add to give $b$ . For $v^2 - 8v + 12$ , we need two numbers that multiply to $12$ and add to $-8$ . The numbers are $-6$ and $-2$ .
Rewrite middle term: Rewrite the middle term using the two numbers found. $\newline$ $8(v^2 - 6v - 2v + 12)$
Factor by grouping: Factor by grouping. $\newline$ $8((v^2 - 6v) - (2v - 12))$
Factor common factors: Factor out the common factors in each group. $8(v(v - 6) - 2(v - 6))$
Factor common binomial: Factor out the common binomial factor. $\newline$ $8(v - 6)(v - 2)$

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