# Problem of the Week

## Updated at Jan 4, 2021 3:18 PM

This week we have another algebra problem:

How can we factor $$8{u}^{2}-20u+12$$?

Let's start!

$8{u}^{2}-20u+12$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$8{u}^{2}$$, $$-20u$$, and $$12$$?It is $$4$$.2 What is the highest degree of $$u$$ that divides evenly into $$8{u}^{2}$$, $$-20u$$, and $$12$$?It is 1, since $$u$$ is not in every term.3 Multiplying the results above,The GCF is $$4$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$4$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$4(\frac{8{u}^{2}}{4}+\frac{-20u}{4}+\frac{12}{4})$3 Simplify each term in parentheses.$4(2{u}^{2}-5u+3)$4 Split the second term in $$2{u}^{2}-5u+3$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times 3=6$2 Ask: Which two numbers add up to $$-5$$ and multiply to $$6$$?$$-2$$ and $$-3$$3 Split $$-5u$$ as the sum of $$-2u$$ and $$-3u$$.$2{u}^{2}-2u-3u+3$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$4(2{u}^{2}-2u-3u+3)$5 Factor out common terms in the first two terms, then in the last two terms.$4(2u(u-1)-3(u-1))$6 Factor out the common term $$u-1$$.$4(u-1)(2u-3)$Done 4*(u-1)*(2*u-3)