Problem of the Week

Updated at Apr 15, 2019 8:45 AM

This week's problem comes from the algebra category.

How can we factor \(36{p}^{2}-6p-30\)?

Let's begin!



\[36{p}^{2}-6p-30\]

1
How?
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.)
\[6(\frac{36{p}^{2}}{6}+\frac{-6p}{6}-\frac{30}{6})\]

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

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

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

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

Done