Problem of the Week

Updated at May 13, 2019 8:42 AM

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May 13, 2019

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

Below is the solution.

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

How?

Find the Greatest Common Factor (GCF).

\[GCF=3\]

Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

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

Simplify each term in parentheses.

\[3(10{v}^{2}-9v+2)\]

How?

Split the second term in \(10{v}^{2}-9v+2\) into two terms.

\[3(10{v}^{2}-4v-5v+2)\]

Factor out common terms in the first two terms, then in the last two terms.

\[3(2v(5v-2)-(5v-2))\]

Factor out the common term \(5v-2\).

\[3(5v-2)(2v-1)\]

Done