Chapter 8.6, Problem 19P

The area of a rectangular parking lot is $21x^2-44x+15.$

The width of the parking lot is $3x-5.$

What is the length of the parking lot?

To determine

To find : the length of the parking lot.

Answer to Problem 19P

  $7x-3$

Explanation of Solution

Given information: The area of a rectangular parking lot is $21x^2-44x+15$ . The width of the book cover is $3x-5$ .

Calculation:

We will factorize the polynomial for the area of the rectangular parking lot by splitting the midle term into two terms whose sum is $-44x$ and product is $315x^2$ .

Therefore, by splitting the middle term , we get

  $\begin{array}{l}21x^2-44x+15\\ =21x^2-35x-9x+15\\ =\left(21x^2-35x\right)+\left(-9x+15\right)\\ =7x\left(3x-5\right)-3\left(3x-5\right)\\ =\left(7x-3\right)\left(3x-5\right)\end{array}$

We know that area of a rectangle is product of its length and width.

Therefore, length of the parking lot is the ratio of its area to its width.

length $=\frac{21x^2-44x+15}{3x-5}=\frac{\left(7x-3\right)\left(3x-5\right)}{3x-5}=7x-3$

Thus, length of the parking lot is $7x-3$ .