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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?
A. X^2-2x-2
B. X^2+2x-2
C. X^2-2x+2
D. X^2+2x+2

Sagot :

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[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.

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.

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