Problem of the Week

Updated at Dec 22, 2025 3:05 PM

This week's problem comes from the algebra category.

How can we compute the factors of \(16{u}^{2}-44u+28\)?

Let's begin!



\[16{u}^{2}-44u+28\]

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.)
\[4(\frac{16{u}^{2}}{4}+\frac{-44u}{4}+\frac{28}{4})\]

3
Simplify each term in parentheses.
\[4(4{u}^{2}-11u+7)\]

4
Split the second term in \(4{u}^{2}-11u+7\) into two terms.
\[4(4{u}^{2}-4u-7u+7)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[4(4u(u-1)-7(u-1))\]

6
Factor out the common term \(u-1\).
\[4(u-1)(4u-7)\]

Done
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