Question

The width,w, of a rectangular garden is X -2 the area of the garden is X^3-2X-4 what is an expression for the length of the garden?
A. X^2-2x-2
B. X^2+2x-2
C. X^2-2x+2
D. X^2+2x+2

Answer 1

$A=wl \Rightarrow l=\frac{A}{w}$
l - length, A - area, w - width

$A=x^3-2x-4 \\ w=x-2 \\ \\ l=\frac{x^3-2x-4}{x-2}=\frac{x^3-2x^2+2x^2-4x+2x-4}{x-2}=\frac{x^2(x-2)+2x(x-2)+2(x-2)}{x-2}=\\ =\frac{(x^2+2x+2)(x-2)}{x-2}=x^2+2x+2$

The answer is D.