Question

factor completely.
$v^{2}-6v - 16$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -16 and add up to -6. The numbers are -8 and 2 since $(-8)\times2=-16$ and $-8 + 2=-6$.

Step2: Rewrite the middle - term

Rewrite $v^{2}-6v - 16$ as $v^{2}-8v+2v - 16$.

Step3: Group the terms

Group the terms: $(v^{2}-8v)+(2v - 16)$.

Step4: Factor out the GCF from each group

Factor out the GCF from each group. From $v^{2}-8v$, the GCF is $v$, so we get $v(v - 8)$. From $2v - 16$, the GCF is 2, so we get $2(v - 8)$.

Step5: Factor out the common binomial factor

Factor out the common binomial factor $(v - 8)$: $(v - 8)(v+2)$.

Answer:

$(v - 8)(v + 2)$