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 36p2−6p−3036{p}^{2}-6p-30?

Let's begin!



36p2−6p−3036{p}^{2}-6p-30

1
Find the Greatest Common Factor (GCF).
GCF = 66

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
6(36p26+−6p6−306)6(\frac{36{p}^{2}}{6}+\frac{-6p}{6}-\frac{30}{6})

3
Simplify each term in parentheses.
6(6p2−p−5)6(6{p}^{2}-p-5)

4
Split the second term in 6p2−p−56{p}^{2}-p-5 into two terms.
6(6p2+5p−6p−5)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(p(6p+5)-(6p+5))

6
Factor out the common term 6p+56p+5.
6(6p+5)(p−1)6(6p+5)(p-1)

Done
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