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:

Set up the area equation

$$ \text{Area} = \text{length} \times \text{width} $$

$$ 5x^2 + 43x - 18 = (x + 9) \times \text{width} $$

Factor the quadratic expression

$$ 5x^2 + 43x - 18 = 5x^2 + 45x - 2x - 18 $$

$$ 5x^2 + 43x - 18 = 5x(x + 9) - 2(x + 9) $$

$$ 5x^2 + 43x - 18 = (5x - 2)(x + 9) $$

Solve for the width

$$ \text{width} = \frac{(5x - 2)(x + 9)}{x + 9} = 5x - 2 $$

Answer:

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 \(x\)?
<blank>\(5x - 2\)</blank>