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).
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.
\[2(2{y}^{2}+3y-8y-12)\]

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
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