# Problem of the Week

## Updated at Jul 10, 2023 9:46 AM

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

How would you find the factors of $$18{p}^{2}-36p-14$$?

Here are the steps:

$18{p}^{2}-36p-14$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$18{p}^{2}$$, $$-36p$$, and $$-14$$?It is $$2$$.2 What is the highest degree of $$p$$ that divides evenly into $$18{p}^{2}$$, $$-36p$$, and $$-14$$?It is 1, since $$p$$ is not in every term.3 Multiplying the results above,The GCF is $$2$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$2$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$2(\frac{18{p}^{2}}{2}+\frac{-36p}{2}-\frac{14}{2})$3 Simplify each term in parentheses.$2(9{p}^{2}-18p-7)$4 Split the second term in $$9{p}^{2}-18p-7$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$9\times -7=-63$2 Ask: Which two numbers add up to $$-18$$ and multiply to $$-63$$?$$3$$ and $$-21$$3 Split $$-18p$$ as the sum of $$3p$$ and $$-21p$$.$9{p}^{2}+3p-21p-7$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(9{p}^{2}+3p-21p-7)$5 Factor out common terms in the first two terms, then in the last two terms.$2(3p(3p+1)-7(3p+1))$6 Factor out the common term $$3p+1$$.$2(3p+1)(3p-7)$Done2*(3*p+1)*(3*p-7)