Chapter 8.5, Problem 62PFA

To determine

To find: The expression which is equivalent to the polynomial $2x^3-10x^2+15-3x$

Answer to Problem 62PFA

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

C is the correct option.

Explanation of Solution

Given:

Options are

  $\begin{array}{l}\mathrm{A }\left(2x^2+3\right)\left(x-5\right)\\ \mathrm{B }\left(2x^2+3\right)\left(x-5\right)\left(5-x\right)\\ \mathrm{C }\left(2x^2-3\right)\left(x-5\right)\\ \mathrm{D }\left(2x^2+3\right){\left(x-5\right)}^2\end{array}$

Calculation:

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

Make group as shown below

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

Now, factored out the GCF from each group

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

Now, factored out the common term

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

Hence, C is the correct option.