Problem of the Week

Updated at Apr 1, 2024 9:48 AM

This week we have another algebra problem:

How can we factor \(20{w}^{2}-38w+14\)?

Let's start!



\[20{w}^{2}-38w+14\]

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.)
\[2(\frac{20{w}^{2}}{2}+\frac{-38w}{2}+\frac{14}{2})\]

3
Simplify each term in parentheses.
\[2(10{w}^{2}-19w+7)\]

4
Split the second term in \(10{w}^{2}-19w+7\) into two terms.
\[2(10{w}^{2}-5w-14w+7)\]

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

6
Factor out the common term \(2w-1\).
\[2(2w-1)(5w-7)\]

Done
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