Question

write an expression for the length of the rectangle. (hint: factor the area binomial and recall that area = width•length.)
area is $6x^5 - 54x$ square units
width: $6x$ units
the length is $square$

Explanation:

Step1: Recall area formula

$Area = width \times length$

Step2: Isolate length variable

$length = \frac{Area}{width}$

Step3: Substitute given expressions

$length = \frac{6x^5 - 54x}{6x}$

Step4: Factor numerator

$6x^5 - 54x = 6x(x^4 - 9)$

Step5: Simplify the fraction

$length = \frac{6x(x^4 - 9)}{6x} = x^4 - 9$

Step6: Factor final expression (optional fully simplified)

$x^4 - 9 = (x^2 + 3)(x^2 - 3)$

Answer:

$x^4 - 9$ (or fully factored: $(x^2 + 3)(x^2 - 3)$)