Question

enter the correct answer in the box.
sharon is paving a rectangular concrete driveway on the side of her house. the area of the driveway is $5x^2 + 43x - 18$, and the length of the driveway is $x + 9$.
what is the width of the driveway in terms of $x$?

Explanation:

Step1: Recall area of rectangle

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \). So, to find the width, we use \( \text{width} = \frac{\text{area}}{\text{length}} \).

Step2: Perform polynomial division or factorization

We need to divide \( 5x^2 + 43x - 18 \) by \( x + 9 \). Let's factor the quadratic:
We look for two numbers that multiply to \( 5 \times (-18) = -90 \) and add to \( 43 \). The numbers are \( 45 \) and \( -2 \).
Rewrite the middle term: \( 5x^2 + 45x - 2x - 18 \)
Factor by grouping: \( 5x(x + 9) - 2(x + 9) = (5x - 2)(x + 9) \)
Now, divide by \( x + 9 \): \( \frac{(5x - 2)(x + 9)}{x + 9} = 5x - 2 \) (since \( x
eq -9 \))

Answer:

\( 5x - 2 \)