Problem of the Week

Updated at Mar 11, 2024 9:46 AM

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

How would you find the factors of \(20{y}^{2}+2y-4\)?

Here are the steps:



\[20{y}^{2}+2y-4\]

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.)
\[2(\frac{20{y}^{2}}{2}+\frac{2y}{2}-\frac{4}{2})\]

3
Simplify each term in parentheses.
\[2(10{y}^{2}+y-2)\]

4
Split the second term in \(10{y}^{2}+y-2\) into two terms.
\[2(10{y}^{2}+5y-4y-2)\]

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

6
Factor out the common term \(2y+1\).
\[2(2y+1)(5y-2)\]

Done
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