Problem of the Week

Updated at May 21, 2018 4:23 PM

This week we have another algebra problem:

How can we compute the factors of \(12{x}^{2}-27x+15\)?

Let's start!



\[12{x}^{2}-27x+15\]

1
Find the Greatest Common Factor (GCF).
GCF = \(3\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[3(\frac{12{x}^{2}}{3}+\frac{-27x}{3}+\frac{15}{3})\]

3
Simplify each term in parentheses.
\[3(4{x}^{2}-9x+5)\]

4
Split the second term in \(4{x}^{2}-9x+5\) into two terms.
\[3(4{x}^{2}-4x-5x+5)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[3(4x(x-1)-5(x-1))\]

6
Factor out the common term \(x-1\).
\[3(x-1)(4x-5)\]

Done
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