How do you factor 5v ^ { 2} - 15v - 90 completely?

2 Answers
Apr 20, 2018

5(v-6)(v+3)

Explanation:

5v^2 - 15v - 90=5(v^2 - 3v - 18)

We want to find two numbers that when added give us 3 and when multiplied give us -18.

The factors of 18 are 2,3,6, and 9.

6-3=3
6 times -3=-18

The numbers 6 and -3 satisfy these two equations.

v^2 - 3v - 18 = (v-6)(v+3)

We can double check this by expanding again.
(v-6)(v+3) = v(v+3)-6(v+3)= v^2 + 3v -6v -18 = v^2 -3v -18

Multiplying all of this by five we get

5(v-6)(v+3)

Apr 20, 2018

5(v-6)(v+3)

Explanation:

"take out a "color(blue)"common factor "5

=5(v^2-3v-18)

"the factors of - 18 which sum to - 3 are - 6 and + 3"

=5(v-6)(v+3)