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 8p2−26p+68{p}^{2}-26p+6?

Here are the steps:



8p2−26p+68{p}^{2}-26p+6

1
Find the Greatest Common Factor (GCF).
GCF = 22

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
2(8p22+−26p2+62)2(\frac{8{p}^{2}}{2}+\frac{-26p}{2}+\frac{6}{2})

3
Simplify each term in parentheses.
2(4p2−13p+3)2(4{p}^{2}-13p+3)

4
Split the second term in 4p2−13p+34{p}^{2}-13p+3 into two terms.
2(4p2−p−12p+3)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))2(p(4p-1)-3(4p-1))

6
Factor out the common term 4p−14p-1.
2(4p−1)(p−3)2(4p-1)(p-3)

Done
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