# Problem of the Week

## Updated at Jun 22, 2020 12:04 PM

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

How would you find the factors of $$12{u}^{2}-26u+4$$?

Check out the solution below!

$12{u}^{2}-26u+4$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$12{u}^{2}$$, $$-26u$$, and $$4$$?It is $$2$$.2 What is the highest degree of $$u$$ that divides evenly into $$12{u}^{2}$$, $$-26u$$, and $$4$$?It is 1, since $$u$$ 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{12{u}^{2}}{2}+\frac{-26u}{2}+\frac{4}{2})$3 Simplify each term in parentheses.$2(6{u}^{2}-13u+2)$4 Split the second term in $$6{u}^{2}-13u+2$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$6\times 2=12$2 Ask: Which two numbers add up to $$-13$$ and multiply to $$12$$?$$-1$$ and $$-12$$3 Split $$-13u$$ as the sum of $$-u$$ and $$-12u$$.$6{u}^{2}-u-12u+2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(6{u}^{2}-u-12u+2)$5 Factor out common terms in the first two terms, then in the last two terms.$2(u(6u-1)-2(6u-1))$6 Factor out the common term $$6u-1$$.$2(6u-1)(u-2)$Done 2*(6*u-1)*(u-2)