Question

the area of a rectangle is given by the expression (x^3+7x^2+11x+2) in^2. The length of the rectangle is given by the expression (x+2) in. What is an expression for the width of the rectangle?

Answer 1

divide (x^3+7x^2+11x+2) by (x+2)
using either long division or synthetic division.
or factor (x^3+7x^2+11x+2) , it does

Answer 2

Reiny is right first you write it as a division problem. But then:
X + 2=0 (solve)
X= -2 or (-2,0)
Then plug the -2 into every spot where there is an X. To check if it can be factored.
(-2)^3+7(-2)^2+11(-2)+2 (type in calculator)
= 0 meaning that (x+2) is a factor