Chapter 8.6, Problem 29PPE

To determine

To simplify: simply the given question using factorization

Answer to Problem 29PPE

The two different values be 2 and 18

Explanation of Solution

Given information: we have given

Trinomial is $15v^2+\square v-24$

Let the unknown value be p

As we know

The sum of factor of -360 will be the value of p

Factor of -360 are (-12,30) and (-18,20)

  $p=30-12=18$ and also $p=20-18=2$

So the two different values of p are 18 and 2

And the trinomials formed will be $15v^2+18v-24$ and $15v^2+2v-24$

Use factoring

  $\begin{array}{c}15v^2+2v-24=15v^2+20v-18v-24\\ =5v\left(3v+4\right)-6\left(3v+4\right)\\ =\left(3v+4\right)\left(5v-6\right)\end{array}$

Therefore the factor is (3v+4) and (5v-6)