Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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 :

naǫ
[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.

View image parmesanchilliwack
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.