Find all zeros of the following polynomial functions, noting multiplicities.

$$f(x)=2 x^6-12 x^5+18 x^4$$

Determine if the function is a polynomial function and, if so, give the degree and leading coefficient.

$$f(x)=5^{x+1}-x^2$$

Use the Remainder Theorem to find the remainder.

$$\left(x^4+5 x^3-4 x-17\right) \div(x+1)$$

Write the polynomial function that models the given situation.

A right circular cone has a radius of $3 x+6$ and a height $3$ units less. Express the volume of the cone as a polynomial function. The volume of a cone is $V=\frac{1}{3} \pi r^2 h$ for radius $r$ and height $h$.

Identify the removable discontinuity.

$$f(x)=\frac{x^3+x^2}{x+1}$$