Problem of the Week

Updated at Dec 30, 2019 1:33 PM

This week we have another algebra problem:

How can we factor \(4{w}^{2}-6w-10\)?

Let's start!



\[4{w}^{2}-6w-10\]

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.)
\[2(\frac{4{w}^{2}}{2}+\frac{-6w}{2}-\frac{10}{2})\]

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

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

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

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

Done
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