Problem of the Week

Updated at Dec 3, 2018 9:51 AM

For this week we've brought you this algebra problem.

How can we factor \(8{p}^{2}-26p+6\)?

Here are the steps:



\[8{p}^{2}-26p+6\]

1
Find the Greatest Common Factor (GCF)
How?

\[GCF=2\]

2
Factor out the GCF (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[2(\frac{8{p}^{2}}{2}+\frac{-26p}{2}+\frac{6}{2})\]

3
Simplify each term in parentheses
\[2(4{p}^{2}-13p+3)\]

4
Split the second term in \(4{p}^{2}-13p+3\) into two terms
How?

\[2(4{p}^{2}-p-12p+3)\]

5
Factor out common terms in the first two terms, then in the last two terms
\[2(p(4p-1)-3(4p-1))\]

6
Factor out the common term \(4p-1\)
\[2(4p-1)(p-3)\]

Done