Chapter 8.6, Problem 56PFA

To determine

To find: The expression that represents the sides of the rectangle.

Answer to Problem 56PFA

  $\left(2x+5\right)\text{ and }\left(3x-6\right)$ .

B is the correct option

Explanation of Solution

Given:

The area of rectangle is represented by the polynomial $6x^2+3x-30$

Options are:

  $\begin{array}{l}\mathrm{A }\left(2x-5\right)\text{ and }\left(3x+6\right)\\ \mathrm{B }\left(2x+5\right)\text{ and }\left(3x-6\right)\\ \mathrm{C }\left(x+4\right)\text{ and }\left(3x+6\right)\\ \mathrm{D }\left(x-27\right)\text{ and }\left(3x-6\right)\end{array}$

Calculation:

The given expression is $6x^2+3x-30$

Factored out the GCF

  $3\left(2x^2+x-10\right)$

Find the factored form of this expression

Write the middle term $x$ as $5x-4x$

  $3\left(2x^2+5x-4x-10\right)$

Make groups as shown below

  $3\left(\left(2x^2+5x\right)+\left(-4x-10\right)\right)$

Factored out the GCF from each group

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

Factored out the common term

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

Rewrite this expression as

  $\left(\left(2x+5\right)\left(3x-6\right)\right)$

The area of a rectangle is length times width.

Hence, the possible expression that represents the sides of the rectangle is

  $\left(2x+5\right)\text{ and }\left(3x-6\right)$

B is the correct option.