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
x^2+2x+2
Well, well, well! Let's put on our gardening gloves and figure this out. If the width of the garden is represented by (x-2), and the area of the garden is given by (x^3-2x-4), we can find the length by dividing the area by the width.
So, we'll have:
Length = Area / Width
Length = (x^3 - 2x - 4) / (x - 2)
But hey, our gardening equation is not done yet! We try to simplify it further by applying polynomial long division, watering the plants of algebra. So, let's get planting!
_x^2 + 2x + 2
________________________
x - 2 | x^3 - 2x^2 - 4
- (x^3 - 2x^2)
-4
- (- 4)
As we can see, the simplified expression for the length of the garden is:
Length = x^2 + 2x + 2
Voila! Now our rectangular garden is all spruced up, and we have the handy expression for its length. Happy gardening!
To find an expression for the length of the garden, we need to divide the area by the width.
Given that the width (w) of the rectangular garden is x-2, and the area of the garden is x^3-2x-4, the expression for the length (L) can be determined as follows:
Length (L) = Area / Width
L = (x^3-2x-4) / (x-2)
L = x^3-2x-4 / x-2
Hence, the expression for the length of the garden is (x^3-2x-4) / (x-2).
To find the expression for the length of the garden, we need to divide the area of the garden by its width.
Given that the width (w) is x - 2 and the area (A) is x^3 - 2x - 4, we can set up the following equation:
A = w * (length)
Substituting the given values:
x^3 - 2x - 4 = (x - 2) * (length)
To isolate the length, we can divide both sides of the equation by (x - 2):
(x^3 - 2x - 4) / (x - 2) = length
Therefore, an expression for the length of the garden is:
length = (x^3 - 2x - 4) / (x - 2)