Question

write an expression for the length of the rectangle (hint: factor the area binomial and recall that area = width • length.) area is 5x^{2}-8x square units

Explanation:

Step1: Recall the area formula

Area = width $\cdot$ length. Given width = $4x^{2}$ and area = $4x^{5}-8x^{2}$.

Step2: Solve for length

Length = $\frac{\text{Area}}{\text{Width}}=\frac{4x^{5}-8x^{2}}{4x^{2}}$.

Step3: Simplify the expression

Using the rule $\frac{a - b}{c}=\frac{a}{c}-\frac{b}{c}$, we have $\frac{4x^{5}}{4x^{2}}-\frac{8x^{2}}{4x^{2}}$.
Applying the rule $\frac{x^{m}}{x^{n}}=x^{m - n}$, we get $x^{5 - 2}-2=x^{3}-2$.

Answer:

$x^{3}-2$ units