 # 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).1 What is the largest number that divides evenly into $$36{p}^{2}$$, $$-6p$$, and $$-30$$?It is $$6$$.2 What is the highest degree of $$p$$ that divides evenly into $$36{p}^{2}$$, $$-6p$$, and $$-30$$?It is 1, since $$p$$ is not in every term.3 Multiplying the results above,The GCF is $$6$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$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.1 Multiply the coefficient of the first term by the constant term.$6\times -5=-30$2 Ask: Which two numbers add up to $$-1$$ and multiply to $$-30$$?$$5$$ and $$-6$$3 Split $$-p$$ as the sum of $$5p$$ and $$-6p$$.$6{p}^{2}+5p-6p-5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$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 6*(6*p+5)*(p-1)