Answer :
[tex]A=lw \Rightarrow l=\frac{A}{w}[/tex]
A - area, l - length, w - width
[tex]w=x-2 \\ A=x^3-2x-4 \\ \\ 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[/tex]
The answer is D. x²+2x+2.
A - area, l - length, w - width
[tex]w=x-2 \\ A=x^3-2x-4 \\ \\ 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[/tex]
The answer is D. x²+2x+2.
Answer:
D. [tex]x^2+2x+2[/tex]
Step-by-step explanation:
We know that,
The area of a rectangle is,
A = l × b,
Where, l is the length of the rectangle,
w is the width of the rectangle,
Given,
[tex]A = x^3-2x-4[/tex]
[tex]w=(x-2)[/tex]
By substituting values,
[tex]x^3-2x-4=(x-2)l[/tex]
[tex]\implies l = \frac{x^3-2x-4}{x-2}=x^2+2x+2[/tex] ( By long division shown below )
Hence, the length of the rectangular garden is [tex]x^2+2x+2[/tex]
Option D is correct.