The area of a rectangle is $2 x ^ { 3 } + 3 x ^ { 2 } - 30 x - 45$ and its length is 2x+3 . Find the width of the rectangle.
A) $2 x ^ { 3 } + 3 x ^ { 2 } - 28 x - 42$
B) $x ^ { 2 } - 30 x + 225$
C) $2 x ^ { 2 } - 30 x - 45$
D) $x ^ { 2 } - 15$
E) $2 x ^ { 3 } + 3 x ^ { 2 } - 30$

Question

Quizplus · Accepted Answer

The width of the rectangle can be found by dividing the area by the length. Given the area $2x^3 + 3x^2 - 30x - 45$ and the length $2x + 3$, the width is $\frac{2x^3 + 3x^2 - 30x - 45}{2x + 3}$. Simplifying this division gives $x^2 - 15$, which corresponds to choice D.

The Area of a Rectangle Is 2x3+3x2−30x−452 x ^ { 3 } + 3 x ^ { 2 } - 30 x - 452x3+3x2−30x−45

The Area of a Rectangle Is $2 x ^ { 3 } + 3 x ^ { 2 } - 30 x - 45$