Name the type of function:

How many solutions are there for the function?

Is the leading coefficient of this polynomial positive or negative?

For the following polynomial, would the end behavior of the graph on the RIGHT side be up or down?

$$f\left(x\right)=-\frac{1}{2}x^6+7x^5-4x^3+9$$  

Is $$\left(x+3\right)$$  a factor of $$2x^3+7x^2-9$$  ? If so, select the other factors.

Which of these is NOT a possible rational root of $$f\left(x\right)=6x^3+x^2-7x+9?$$  

Hint: Make a p/q list.

Bobby solved the polynomial $$f\left(x\right)=x^6+x^3-7x^2-8x+1$$   and got 3 real solutions and 3 imaginary solutions. Is this possible? Why?

Find the other roots of the function, $$f\left(x\right)=x^3+2x^2-5x-6$$  , given that one of its roots is $$x=-3$$  .

Find the other roots of the function, $$f\left(x\right)=x^3-5x^2-3x+15$$  , given that one of its roots is $$x=-\ \sqrt[\ ]{3}$$  .

Using the Rational Roots Theorem (p/q) and/or Desmos, find all roots for the function: $$f\left(x\right)=2x^3-3x^2+8x-12$$  .

A videogame company models profit using the following function, $$p\left(x\right)=-2x^3+9x^2+11x-30$$  , where the number of games produced (x) and profit (p(x)) are both in millions.

Between what values of games does the company make a profit? Also, what is the maximum profit they can make?

Use Desmos to create a graph.