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).
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.
\[6(3{y}^{2}+3y-4y-4)\]

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 \(y+1\).
\[6(y+1)(3y-4)\]

Done
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