Question

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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 rectangle area formula

Area = Length × Width, so Width = $\frac{\text{Area}}{\text{Length}}$

Step2: Substitute given expressions

Width = $\frac{5x^2 + 43x - 18}{x + 9}$

Step3: Factor the quadratic numerator

Find two numbers: $45$ and $-2$, since $45 \times (-2) = -90$ and $45 + (-2) = 43$.
$5x^2 + 43x - 18 = 5x^2 + 45x - 2x - 18 = 5x(x + 9) - 2(x + 9) = (5x - 2)(x + 9)$

Step4: Simplify the fraction

Cancel $(x + 9)$ from numerator and denominator:
Width = $\frac{(5x - 2)(x + 9)}{x + 9} = 5x - 2$

Answer:

$5x - 2$