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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?

AX^2-2x-2
BX^2+2x-2
CX^2-2x+2
DX^2+2x+2

Verified Answer :

naǫ

\(A=wl \Rightarrow l=\frac{A}{w}\)
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.

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