# Problem of the Week

## Updated at Nov 20, 2023 10:25 AM

This week's problem comes from the algebra category.

How would you find the factors of $$18{y}^{2}-6y-24$$?

Let's begin!

$18{y}^{2}-6y-24$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$18{y}^{2}$$, $$-6y$$, and $$-24$$?It is $$6$$.2 What is the highest degree of $$y$$ that divides evenly into $$18{y}^{2}$$, $$-6y$$, and $$-24$$?It is 1, since $$y$$ is not in every term.3 Multiplying the results above,The GCF is $$6$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$6$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$6(\frac{18{y}^{2}}{6}+\frac{-6y}{6}-\frac{24}{6})$3 Simplify each term in parentheses.$6(3{y}^{2}-y-4)$4 Split the second term in $$3{y}^{2}-y-4$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$3\times -4=-12$2 Ask: Which two numbers add up to $$-1$$ and multiply to $$-12$$?$$3$$ and $$-4$$3 Split $$-y$$ as the sum of $$3y$$ and $$-4y$$.$3{y}^{2}+3y-4y-4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$6(3{y}^{2}+3y-4y-4)$5 Factor out common terms in the first two terms, then in the last two terms.$6(3y(y+1)-4(y+1))$6 Factor out the common term $$y+1$$.$6(y+1)(3y-4)$Done6*(y+1)*(3*y-4)