Problem of the Week

Updated at May 17, 2021 11:07 AM

How would you find the factors of 30v224v630{v}^{2}-24v-6?

Below is the solution.



30v224v630{v}^{2}-24v-6

1
Find the Greatest Common Factor (GCF).
GCF = 66

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
6(30v26+24v666)6(\frac{30{v}^{2}}{6}+\frac{-24v}{6}-\frac{6}{6})

3
Simplify each term in parentheses.
6(5v24v1)6(5{v}^{2}-4v-1)

4
Split the second term in 5v24v15{v}^{2}-4v-1 into two terms.
6(5v2+v5v1)6(5{v}^{2}+v-5v-1)

5
Factor out common terms in the first two terms, then in the last two terms.
6(v(5v+1)(5v+1))6(v(5v+1)-(5v+1))

6
Factor out the common term 5v+15v+1.
6(5v+1)(v1)6(5v+1)(v-1)

Done