Problem of the Week

Updated at Aug 3, 2026 1:00 PM

This week's problem comes from the algebra category.

How can we factor \(30{q}^{2}-44q+16\)?

Let's begin!



\[30{q}^{2}-44q+16\]

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.)
\[2(\frac{30{q}^{2}}{2}+\frac{-44q}{2}+\frac{16}{2})\]

3
Simplify each term in parentheses.
\[2(15{q}^{2}-22q+8)\]

4
Split the second term in \(15{q}^{2}-22q+8\) into two terms.
\[2(15{q}^{2}-10q-12q+8)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[2(5q(3q-2)-4(3q-2))\]

6
Factor out the common term \(3q-2\).
\[2(3q-2)(5q-4)\]

Done
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