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 shows a seventh-degree polynomial: (graph below)
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).