Problem of the Week

Updated at Dec 18, 2017 3:47 PM

How can we compute the factors of \(18{x}^{2}-24x+6\)?

Below is the solution.



\[18{x}^{2}-24x+6\]

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.)
\[6(\frac{18{x}^{2}}{6}+\frac{-24x}{6}+\frac{6}{6})\]

3
Simplify each term in parentheses.
\[6(3{x}^{2}-4x+1)\]

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

5
Factor out common terms in the first two terms, then in the last two terms.
\[6(x(3x-1)-(3x-1))\]

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

Done
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