Chapter 8.5, Problem 65PFA

To determine

To find: The sum of the two binomials.

Answer to Problem 65PFA

  $x^2+2x-8$

Explanation of Solution

Given:

The product of two binomials is $2x^3-3x^2-10x+15$

Calculation:

The given polynomial is $2x^3-3x^2-10x+15$

Find the factored form of this polynomial

Make group as shown below

  $\left(2x^3-3x^2\right)+\left(-10x+15\right)$

Now, factored out the GCF from each group

  $x^2\left(2x-3\right)-5\left(2x-3\right)$

Now, factored out the common term

  $\left(x^2-5\right)\left(2x-3\right)$

So, the sum of these binomials is given by

  $\begin{array}{l}\left(x^2-5\right)+\left(2x-3\right)\\ =x^2+2x-5-3\\ =x^2+2x-8\end{array}$