Question

factor completely.
$5v^2 + 45v + 90$

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(5v^2\), \(45v\), and \(90\) is \(5\). So we factor out \(5\):
\(5v^2 + 45v + 90 = 5(v^2 + 9v + 18)\)

Step2: Factor the quadratic trinomial

We need to factor \(v^2 + 9v + 18\). We look for two numbers that multiply to \(18\) and add up to \(9\). The numbers are \(6\) and \(3\) (since \(6\times3 = 18\) and \(6 + 3 = 9\)). So we can write:
\(v^2 + 9v + 18 = (v + 6)(v + 3)\)

Step3: Combine the factors

Substituting the factored form of the quadratic back into the expression from Step1, we get:
\(5(v + 6)(v + 3)\)

Answer:

\(5(v + 6)(v + 3)\)