Question

factor completely.
( v^2 - 3v - 18 )

Explanation:

Step1: Analyze the quadratic expression

We have the quadratic expression \(v^2 - 3v - 18\). We need to find two numbers that multiply to \(- 18\) and add up to \(-3\).
Let's list the factor pairs of \(-18\): \((-6)\times3=-18\) and \(-6 + 3=-3\)

Step2: Factor the quadratic

Using the two numbers we found, we can rewrite the middle term of the quadratic expression:
\(v^2 - 3v - 18=v^2-6v + 3v-18\)
Now, we group the terms:
\(=(v^2 - 6v)+(3v - 18)\)
Factor out the greatest common factor from each group:
\(=v(v - 6)+3(v - 6)\)
Now, we can factor out the common binomial factor \((v - 6)\):
\(=(v - 6)(v + 3)\)

Answer:

\((v - 6)(v + 3)\)