# Problem of the Week

## Updated at Jun 7, 2021 3:43 PM

This week we have another algebra problem:

How would you find the factors of $$4{y}^{2}-10y-24$$?

Let's start!

$4{y}^{2}-10y-24$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$4{y}^{2}$$, $$-10y$$, and $$-24$$?It is $$2$$.2 What is the highest degree of $$y$$ that divides evenly into $$4{y}^{2}$$, $$-10y$$, and $$-24$$?It is 1, since $$y$$ 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{4{y}^{2}}{2}+\frac{-10y}{2}-\frac{24}{2})$3 Simplify each term in parentheses.$2(2{y}^{2}-5y-12)$4 Split the second term in $$2{y}^{2}-5y-12$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times -12=-24$2 Ask: Which two numbers add up to $$-5$$ and multiply to $$-24$$?$$3$$ and $$-8$$3 Split $$-5y$$ as the sum of $$3y$$ and $$-8y$$.$2{y}^{2}+3y-8y-12$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(2{y}^{2}+3y-8y-12)$5 Factor out common terms in the first two terms, then in the last two terms.$2(y(2y+3)-4(2y+3))$6 Factor out the common term $$2y+3$$.$2(2y+3)(y-4)$Done 2*(2*y+3)*(y-4)