Solve.
-If the area of a rectangle is $\left( 2 x ^ { 4 } + 11 x ^ { 3 } - 10 x ^ { 2 } - 93 x - 90 \right)$ square inches, and its width is $( 2 x + 3 )$ inches, find its length.
A) $x ^ { 3 } + 4 x ^ { 2 } - 11 x - 30$ in.
B) $x ^ { 3 } - 10 x ^ { 2 } + 5 x - 30$ in.
C) $x ^ { 3 } - 11 x ^ { 2 } + 4 x - 30$ in.
D) $x ^ { 3 } + 5 x ^ { 2 } - 10 x - 30$ in.

Question

Quizplus · Accepted Answer

To find the length of the rectangle, divide the area by the width: $\frac{2 x ^ { 4 } + 11 x ^ { 3 } - 10 x ^ { 2 } - 93 x - 90}{2 x + 3}$. Performing polynomial division or using synthetic division, the quotient is $x ^ { 3 } + 4 x ^ { 2 } - 11 x - 30$, which matches choice A.

Solve -If the Area of a Rectangle Is (2x4+11x3−10x2−93x−90)\left( 2 x ^ { 4 } + 11 x ^ { 3 } - 10 x ^ { 2 } - 93 x - 90 \right)(2x4+11x3−10x2−93x−90)

Solve
-If the Area of a Rectangle Is $\left( 2 x ^ { 4 } + 11 x ^ { 3 } - 10 x ^ { 2 } - 93 x - 90 \right)$