Question

write an expression for the length of the rectangle. (hint: factor the area binomial and recall that area = width · length)
area = 4x³ - 36x²
width =?
length =?
to find a:
...

Explanation:

Step1: Recall area formula

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

Step2: Substitute given expressions

$\text{length} = \frac{4x^3 - 28x^2}{4x^2}$

Step3: Factor numerator

$\text{length} = \frac{4x^2(x - 7)}{4x^2}$

Step4: Cancel common terms

$\text{length} = x - 7$

Answer:

$x - 7$ units