Chapter 8.5, Problem 57PFA

To determine

To find: The dimensions of the rectangle.

Answer to Problem 57PFA

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

Explanation of Solution

Given:

The area of rectangle is given by $10x^3+15x^2+4x+6$

Calculation:

Factor the given polynomial $10x^3+15x^2+4x+6$

Make groups as shown below

  $\left(10x^3+15x^2\right)+\left(4x+6\right)$

Factored out the GCF from each group

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

Factored out the common term

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

The area of the rectangle is the product of the length and the width.

Hence, the dimensions of the rectangle are $\left(5x^2+2\right)\text{ and }\left(2x+3\right)$