The area of a rectangle is 2 x 3 + 3 x 2 − 30 x − 45 2 x ^ { 3 } + 3 x ^ { 2 } - 30 x - 45 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 2 x ^ { 3 } + 3 x ^ { 2 } - 28 x - 42 2 x 3 + 3 x 2 − 28 x − 42 B) x 2 − 30 x + 225 x ^ { 2 } - 30 x + 225 x 2 − 30 x + 225 C) 2 x 2 − 30 x − 45 2 x ^ { 2 } - 30 x - 45 2 x 2 − 30 x − 45 D) x 2 − 15 x ^ { 2 } - 15 x 2 − 15 E) 2 x 3 + 3 x 2 − 30 2 x ^ { 3 } + 3 x ^ { 2 } - 30 2 x 3 + 3 x 2 − 30

Question

The area of a rectangle is   2 x 3 + 3 x 2 − 30 x − 45 2 x ^ { 3 } + 3 x ^ { 2 } - 30 x - 45 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 2 x ^ { 3 } + 3 x ^ { 2 } - 28 x - 42 2 x 3 + 3 x 2 − 28 x − 42 B)    x 2 − 30 x + 225 x ^ { 2 } - 30 x + 225 x 2 − 30 x + 225 C)    2 x 2 − 30 x − 45 2 x ^ { 2 } - 30 x - 45 2 x 2 − 30 x − 45 D)    x 2 − 15 x ^ { 2 } - 15 x 2 − 15 E)    2 x 3 + 3 x 2 − 30 2 x ^ { 3 } + 3 x ^ { 2 } - 30 2 x 3 + 3 x 2 − 30

joshua winston · Accepted Answer

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

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) $2 x ^ { 3 } + 3 x ^ { 2 } - 30$

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