The width, w, of a rectangular playground is x plus 3. The area of the playground is x cubed minus 7 times x plus 6 . What is an expression for the length of the playground?
We know that the area of a rectangle is given by the formula A = lw, where A is the area, l is the length, and w is the width. We are given that the width is x+3 and the area is x^3 - 7x + 6. So we can set up the equation:
x^3 - 7x + 6 = (x+3)l
To solve for l, we can divide both sides by x+3:
l = (x^3 - 7x + 6) / (x+3)
Therefore, an expression for the length of the playground is (x^3 - 7x + 6) / (x+3).
pls simplify (x^3 - 7x + 6) / (x+3)
We can simplify the expression using polynomial division or synthetic division. The result is:
x^2 - 3x + 2
Therefore, (x^3 - 7x + 6) / (x+3) simplifies to x^2 - 3x + 2.
To find the expression for the length of the playground, we'll use the formula for calculating the area of a rectangle, which is length multiplied by width.
Given:
Width, w = x + 3
Area = x^3 - 7x + 6
Since Area = length * width, we can rearrange the formula to solve for the length:
Length * Width = Area
Length * (x + 3) = x^3 - 7x + 6
Now, solve for the length:
Length = (x^3 - 7x + 6) / (x + 3)
Therefore, an expression for the length of the playground is:
Length = (x^3 - 7x + 6) / (x + 3)