Problem of the Week

Updated at Jun 16, 2025 12:11 PM

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

How can we compute the factors of \(20{y}^{2}-8y-12\)?

Here are the steps:



\[20{y}^{2}-8y-12\]

1
Find the Greatest Common Factor (GCF).
GCF = \(4\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[4(\frac{20{y}^{2}}{4}+\frac{-8y}{4}-\frac{12}{4})\]

3
Simplify each term in parentheses.
\[4(5{y}^{2}-2y-3)\]

4
Split the second term in \(5{y}^{2}-2y-3\) into two terms.
\[4(5{y}^{2}+3y-5y-3)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[4(y(5y+3)-(5y+3))\]

6
Factor out the common term \(5y+3\).
\[4(5y+3)(y-1)\]

Done
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