Problem of the Week

Updated at Oct 29, 2018 9:27 AM

How can we factor \(6{x}^{2}+33x-18\)?

Below is the solution.



\[6{x}^{2}+33x-18\]

1
Find the Greatest Common Factor (GCF)
How?

\[GCF=3\]

2
Factor out the GCF (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[3(\frac{6{x}^{2}}{3}+\frac{33x}{3}-\frac{18}{3})\]

3
Simplify each term in parentheses
\[3(2{x}^{2}+11x-6)\]

4
Split the second term in \(2{x}^{2}+11x-6\) into two terms
How?

\[3(2{x}^{2}+12x-x-6)\]

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

6
Factor out the common term \(x+6\)
\[3(x+6)(2x-1)\]

Done