Question

factor completely.
$6v^2 + 24v - 72$

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(6v^2\), \(24v\), and \(-72\) is 6. So we factor out 6:
\(6v^2 + 24v - 72 = 6(v^2 + 4v - 12)\)

Step2: Factor the quadratic

Now we factor the quadratic \(v^2 + 4v - 12\). We need two numbers that multiply to \(-12\) and add to \(4\). Those numbers are \(6\) and \(-2\). So we can write:
\(v^2 + 4v - 12 = (v + 6)(v - 2)\)

Step3: Combine the factors

Putting it all together, the completely factored form is:
\(6(v + 6)(v - 2)\)

Answer:

\(6(v + 6)(v - 2)\)