Chapter 8.6, Problem 28PPE

To determine

To simplify: simply the given question using factorization

Answer to Problem 28PPE

The two different values be 13 and 14

Explanation of Solution

Given information: we have given

Trinomial is $4s^2+\square s+10$

Let the unknown value be p

As we know

The sum of factor of 40 will be the value of p

Factor of 40 are (8,5) and (10,4)

p=8+5=13 and also p=10+4=14

So the two different values of p are 13 and 14

And the trinomials formed will be $4s^2+13s+10$ and $4s^2+14s+10$

Use factoring

  $\begin{array}{c}4s^2+13s+10=4s^2+8s+5s+10\\ =4s\left(s+2\right)+5\left(s+2\right)\\ =\left(4s+5\right)\left(s+2\right)\end{array}$

Therefore the factor is (4s+5) and (s+2)