# Problem of the Week

## Updated at Oct 18, 2021 8:24 AM

To get more practice in algebra, we brought you this problem of the week:

How can we factor $$30{m}^{2}-26m+4$$?

Check out the solution below!

$30{m}^{2}-26m+4$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$30{m}^{2}$$, $$-26m$$, and $$4$$?It is $$2$$.2 What is the highest degree of $$m$$ that divides evenly into $$30{m}^{2}$$, $$-26m$$, and $$4$$?It is 1, since $$m$$ 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{30{m}^{2}}{2}+\frac{-26m}{2}+\frac{4}{2})$3 Simplify each term in parentheses.$2(15{m}^{2}-13m+2)$4 Split the second term in $$15{m}^{2}-13m+2$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$15\times 2=30$2 Ask: Which two numbers add up to $$-13$$ and multiply to $$30$$?$$-3$$ and $$-10$$3 Split $$-13m$$ as the sum of $$-3m$$ and $$-10m$$.$15{m}^{2}-3m-10m+2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(15{m}^{2}-3m-10m+2)$5 Factor out common terms in the first two terms, then in the last two terms.$2(3m(5m-1)-2(5m-1))$6 Factor out the common term $$5m-1$$.$2(5m-1)(3m-2)$Done 2*(5*m-1)*(3*m-2)