# Problem of the Week

## Updated at Jun 5, 2023 9:31 AM

For this week we've brought you this algebra problem.

How would you find the factors of $$20{u}^{2}+4u-24$$?

Here are the steps:

$20{u}^{2}+4u-24$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$20{u}^{2}$$, $$4u$$, and $$-24$$?It is $$4$$.2 What is the highest degree of $$u$$ that divides evenly into $$20{u}^{2}$$, $$4u$$, and $$-24$$?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{20{u}^{2}}{4}+\frac{4u}{4}-\frac{24}{4})$3 Simplify each term in parentheses.$4(5{u}^{2}+u-6)$4 Split the second term in $$5{u}^{2}+u-6$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$5\times -6=-30$2 Ask: Which two numbers add up to $$1$$ and multiply to $$-30$$?$$6$$ and $$-5$$3 Split $$u$$ as the sum of $$6u$$ and $$-5u$$.$5{u}^{2}+6u-5u-6$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$4(5{u}^{2}+6u-5u-6)$5 Factor out common terms in the first two terms, then in the last two terms.$4(u(5u+6)-(5u+6))$6 Factor out the common term $$5u+6$$.$4(5u+6)(u-1)$Done 4*(5*u+6)*(u-1)