Problem of the Week

Updated at May 17, 2021 11:07 AM

How would you find the factors of \(30{v}^{2}-24v-6\)?

Below is the solution.



\[30{v}^{2}-24v-6\]

1
Find the Greatest Common Factor (GCF).
GCF = \(6\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[6(\frac{30{v}^{2}}{6}+\frac{-24v}{6}-\frac{6}{6})\]

3
Simplify each term in parentheses.
\[6(5{v}^{2}-4v-1)\]

4
Split the second term in \(5{v}^{2}-4v-1\) into two terms.
\[6(5{v}^{2}+v-5v-1)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[6(v(5v+1)-(5v+1))\]

6
Factor out the common term \(5v+1\).
\[6(5v+1)(v-1)\]

Done
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