# Problem of the Week

## Updated at Nov 6, 2023 1:33 PM

This week we have another algebra problem:

How can we factor $$36{v}^{2}-66v+30$$?

Let's start!

$36{v}^{2}-66v+30$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$36{v}^{2}$$, $$-66v$$, and $$30$$?It is $$6$$.2 What is the highest degree of $$v$$ that divides evenly into $$36{v}^{2}$$, $$-66v$$, and $$30$$?It is 1, since $$v$$ 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{v}^{2}}{6}+\frac{-66v}{6}+\frac{30}{6})$3 Simplify each term in parentheses.$6(6{v}^{2}-11v+5)$4 Split the second term in $$6{v}^{2}-11v+5$$ 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 $$-11$$ and multiply to $$30$$?$$-5$$ and $$-6$$3 Split $$-11v$$ as the sum of $$-5v$$ and $$-6v$$.$6{v}^{2}-5v-6v+5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$6(6{v}^{2}-5v-6v+5)$5 Factor out common terms in the first two terms, then in the last two terms.$6(v(6v-5)-(6v-5))$6 Factor out the common term $$6v-5$$.$6(6v-5)(v-1)$Done6*(6*v-5)*(v-1)