Problem of the Week

Updated at Sep 9, 2024 5:53 PM

This week we have another algebra problem:

How can we compute the factors of \(42{q}^{2}-60q+18\)?

Let's start!



\[42{q}^{2}-60q+18\]

1
Find the Greatest Common Factor (GCF).
GCF = \(6\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[6(\frac{42{q}^{2}}{6}+\frac{-60q}{6}+\frac{18}{6})\]

3
Simplify each term in parentheses.
\[6(7{q}^{2}-10q+3)\]

4
Split the second term in \(7{q}^{2}-10q+3\) into two terms.
\[6(7{q}^{2}-3q-7q+3)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[6(q(7q-3)-(7q-3))\]

6
Factor out the common term \(7q-3\).
\[6(7q-3)(q-1)\]

Done
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