A rectangular room has a floor space of $\left( x ^ { 2 } + 5 x + 6 \right)$ square feet. If the width of the room is $( x + 2 )$ feet, what is the length?
A) $( x - 3 )$ feet
B) $( x + 3 )$ feet
C) $( 3 x + 1 )$ feet
D) $( 3 x - 1 )$ feet
E) $( x - 2 )$ feet

Question

Quizplus · Accepted Answer

The area of a rectangle is given by the formula length $\times$ width. Given the area $(x^2 + 5x + 6)$ and the width $(x + 2)$, we can find the length by dividing the area by the width: $\frac{x^2 + 5x + 6}{x + 2}$. Factoring the numerator, we get $(x + 3)(x + 2)$. Dividing by $(x + 2)$ leaves $(x + 3)$ as the length.

A Rectangular Room Has a Floor Space Of (x2+5x+6)\left( x ^ { 2 } + 5 x + 6 \right)(x2+5x+6)

A Rectangular Room Has a Floor Space Of $\left( x ^ { 2 } + 5 x + 6 \right)$