Problem of the Week

Updated at Dec 17, 2018 11:09 AM

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

How can we factor \(36{v}^{2}-48v+15\)?

Check out the solution below!



\[36{v}^{2}-48v+15\]

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.)
\[3(\frac{36{v}^{2}}{3}+\frac{-48v}{3}+\frac{15}{3})\]

3
Simplify each term in parentheses.
\[3(12{v}^{2}-16v+5)\]

4
How?
Split the second term in \(12{v}^{2}-16v+5\) into two terms.
\[3(12{v}^{2}-6v-10v+5)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[3(6v(2v-1)-5(2v-1))\]

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

Done