# Problem of the Week

## Updated at May 17, 2021 11:07 AM

How would you find the factors of $$30{v}^{2}-24v-6$$?

Below is the solution.

$30{v}^{2}-24v-6$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$30{v}^{2}$$, $$-24v$$, and $$-6$$?It is $$6$$.2 What is the highest degree of $$v$$ that divides evenly into $$30{v}^{2}$$, $$-24v$$, and $$-6$$?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{30{v}^{2}}{6}+\frac{-24v}{6}-\frac{6}{6})$3 Simplify each term in parentheses.$6(5{v}^{2}-4v-1)$4 Split the second term in $$5{v}^{2}-4v-1$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$5\times -1=-5$2 Ask: Which two numbers add up to $$-4$$ and multiply to $$-5$$?$$1$$ and $$-5$$3 Split $$-4v$$ as the sum of $$v$$ and $$-5v$$.$5{v}^{2}+v-5v-1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$6(5{v}^{2}+v-5v-1)$5 Factor out common terms in the first two terms, then in the last two terms.$6(v(5v+1)-(5v+1))$6 Factor out the common term $$5v+1$$.$6(5v+1)(v-1)$Done6*(5*v+1)*(v-1)