Using the Fundamental Theorem of Algebra, complete the following exercises. Show your work. 1. Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.

2. Determine how many, what type, and find the roots for f(x) = x3 − 5x2 − 25x + 125.

3. The following graph below shows a seventh-degree polynomial:

Part 1: List the polynomial’s zeroes with possible multiplicities.

Part 2: Write a possible factored form of the seventh-degree function.

4. Without plotting any points other than intercepts, draw a possible graph of the following polynomial: f(x) = (x + 8)3 (x + 6)2 (x + 2)(x − 1)3 (x − 3)4 (x − 6).