Question

factor completely.
6v² + 48v - 54

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(6v^2\), \(48v\), and \(-54\) is 6. So we factor out 6:
\(6v^2 + 48v - 54 = 6(v^2 + 8v - 9)\)

Step2: Factor the quadratic

We need to factor \(v^2 + 8v - 9\). We look for two numbers that multiply to \(-9\) and add to 8. The numbers are 9 and -1.
So \(v^2 + 8v - 9=(v + 9)(v - 1)\)

Step3: Combine the factors

Putting it all together, we have:
\(6v^2 + 48v - 54 = 6(v + 9)(v - 1)\)

Answer:

\(6(v + 9)(v - 1)\)