the area of a rectangle is given by the expression (x^3+7x^2+11x+2) in^2. The length of the rectangle is given by the expression (x+2) in. What is an expression for the width of the rectangle?
Reiny is right first you write it as a division problem. But then:
X + 2=0 (solve)
X= -2 or (-2,0)
Then plug the -2 into every spot where there is an X. To check if it can be factored.
(-2)^3+7(-2)^2+11(-2)+2 (type in calculator)
= 0 meaning that (x+2) is a factor
Well, to find the width of the rectangle, we can use the formula for the area of a rectangle: Area = Length × Width.
Given that the area is (x^3 + 7x^2 + 11x + 2) in^2 and the length is (x + 2) in, we can use the formula to express the width.
So, solving for the width, we have:
Width = Area / Length
Width = (x^3 + 7x^2 + 11x + 2) in^2 / (x + 2) in
However, I must warn you that this rectangle is quite sensitive about their width. Make sure not to mention the word "narrow" around it, or it might get offended!
To find an expression for the width of the rectangle, we can divide the area expression by the length expression.
Dividing the area (x^3+7x^2+11x+2) by the length (x+2), we get:
(x^3+7x^2+11x+2)/(x+2)
Using polynomial long division, we find that the result is:
x^2 + 5x + 1
Therefore, the expression for the width of the rectangle is:
x^2 + 5x + 1 inches.
To find an expression for the width of the rectangle, we can use the formula for the area of a rectangle:
Area = Length x Width
In this case, the area of the rectangle is given by the expression (x^3 + 7x^2 + 11x + 2) in^2, and the length is given by the expression (x + 2) in. Let's denote the width as 'w' (inches).
Now we can set up an equation:
(x^3 + 7x^2 + 11x + 2) = (x + 2) * w
To solve for 'w', we can divide both sides of the equation by (x + 2):
w = (x^3 + 7x^2 + 11x + 2) / (x + 2)
Therefore, an expression for the width of the rectangle is (x^3 + 7x^2 + 11x + 2) / (x + 2).
divide (x^3+7x^2+11x+2) by (x+2)
using either long division or synthetic division.
or factor (x^3+7x^2+11x+2) , it does