The area of a rectangle is given by the expression x2 + 5x + 4. if the length of one side is given by x + 2, what is the length of the other side?

Excuse the correction, but "the square of x" should be typed as "x^2." 

"x2" is ambiguous.  Some people would interpret it as "x times 2," which is incorrect here.

Recall that "area of a rectangle = (length) * (width).

Here the area is x^2+5x+4, and the length of one side is x+2.  How woud you determine the width of the rectangle?