Problem of the Week

Updated at Apr 8, 2024 1:34 PM

To get more practice in algebra, we brought you this problem of the week:

How would you find the factors of \(12{m}^{2}-18m+6\)?

Check out the solution below!



\[12{m}^{2}-18m+6\]

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.)
\[6(\frac{12{m}^{2}}{6}+\frac{-18m}{6}+\frac{6}{6})\]

3
Simplify each term in parentheses.
\[6(2{m}^{2}-3m+1)\]

4
Split the second term in \(2{m}^{2}-3m+1\) into two terms.
\[6(2{m}^{2}-m-2m+1)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[6(m(2m-1)-(2m-1))\]

6
Factor out the common term \(2m-1\).
\[6(2m-1)(m-1)\]

Done
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