Problem of the Week

Updated at May 26, 2025 10:11 AM

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

How can we compute the factors of \(42{y}^{2}-22y-4\)?

Here are the steps:



\[42{y}^{2}-22y-4\]

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.)
\[2(\frac{42{y}^{2}}{2}+\frac{-22y}{2}-\frac{4}{2})\]

3
Simplify each term in parentheses.
\[2(21{y}^{2}-11y-2)\]

4
Split the second term in \(21{y}^{2}-11y-2\) into two terms.
\[2(21{y}^{2}+3y-14y-2)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[2(3y(7y+1)-2(7y+1))\]

6
Factor out the common term \(7y+1\).
\[2(7y+1)(3y-2)\]

Done
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