Let the function \(P\) be defined by \(P(x) = x^3 + 2x^2 - 13x + 10\). Mai divides \(P(x)\) by \(x+5\) and gets:

For the polynomial function \(f(x)=x^4+3x^3-x^2-3x\), we have \(f(\text-3)= 0, f(\text-2)=\text-6, f(\text-1)=0\), \(f(0)=0, f(1)=0,f(2)=30, f(3)=144\). Rewrite \(f(x)\) as a product of linear factors.

There are many cones with a volume of \(60\pi\) cubic inches. The height \(h(r)\), in inches, of one of these cones is a function of its radius \(r\), in inches, where \(h(r)=\frac{180}{r^2}\).

1. What is the height of one of these cones if its radius is 2 inches?
2. What is the height of one of these cones if its radius is 3 inches?
3. What is the height of one of these cones if its radius is 6 inches?

A cylindrical can needs to have a volume of 10 cubic inches. There needs to be a label around the side of the can. The function \(S(r)=\frac{20}{r}\) gives the area of the label in square inches, where \(r\) is the radius of the can in inches.

1. As \(r\) gets closer and closer to 0, what does the behavior of the function tell you about the situation?

2. As \(r\) gets larger and larger, what does the end behavior of the function tell you about the situation?

Match each rational function with a description of its end behavior as \(x\) gets larger and larger.