Problem of the Week

Updated at May 13, 2019 8:42 AM

How can we factor \(30{v}^{2}-27v+6\)?

Below is the solution.



\[30{v}^{2}-27v+6\]

1
How?
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.)
\[3(\frac{30{v}^{2}}{3}+\frac{-27v}{3}+\frac{6}{3})\]

3
Simplify each term in parentheses.
\[3(10{v}^{2}-9v+2)\]

4
How?
Split the second term in \(10{v}^{2}-9v+2\) into two terms.
\[3(10{v}^{2}-4v-5v+2)\]

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

6
Factor out the common term \(5v-2\).
\[3(5v-2)(2v-1)\]

Done