# Problem of the Week

## Updated at Jul 4, 2022 8:55 AM

This week's problem comes from the algebra category.

How would you find the factors of $$15{n}^{2}+10n-5$$?

Let's begin!

$15{n}^{2}+10n-5$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$15{n}^{2}$$, $$10n$$, and $$-5$$?It is $$5$$.2 What is the highest degree of $$n$$ that divides evenly into $$15{n}^{2}$$, $$10n$$, and $$-5$$?It is 1, since $$n$$ is not in every term.3 Multiplying the results above,The GCF is $$5$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$5$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$5(\frac{15{n}^{2}}{5}+\frac{10n}{5}-\frac{5}{5})$3 Simplify each term in parentheses.$5(3{n}^{2}+2n-1)$4 Split the second term in $$3{n}^{2}+2n-1$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$3\times -1=-3$2 Ask: Which two numbers add up to $$2$$ and multiply to $$-3$$?$$3$$ and $$-1$$3 Split $$2n$$ as the sum of $$3n$$ and $$-n$$.$3{n}^{2}+3n-n-1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$5(3{n}^{2}+3n-n-1)$5 Factor out common terms in the first two terms, then in the last two terms.$5(3n(n+1)-(n+1))$6 Factor out the common term $$n+1$$.$5(n+1)(3n-1)$Done 5*(n+1)*(3*n-1)