1. The Fundamental Theorem of Algebra
1. Tada! It's the Fundamental Theorem of Algebra. It's no big surprise, though, as Mrs. Gould taught it to us during Section 4. The theorem simply states that the degree of any polynomial is how many solutions it has.
2. Remember though, the solutions may not all be real, and solutions that are real may be irrational.

2. Finding the Zeroes of Polynomial Functions
1. Once again, this is not new material. Now, before you use the zero product property, make sure that you factor out complex numbers, too.

3. Writing Polynomial Functions with Given Factors
1. We've been factoring polynomial functions for the whole chapter, but how do the textbook writers make polynomial functions that factor?
2. First, it is necessary to understand that anything with a factor of a square root has at least two factors, one positive and one negative.
3. Since i is the square root of -1, anything that has i for a factor also of -i.
4. With that in mind, writing polynomial functions with given factors is easy. Just multiply all the factors together. The product is the polynomial of least degree and a with a leading coefficient of 1 that has all the factors.

Find all the zeroes of the function.

1. f(x) = x² + 1
2. f(x) = x³ + 4x² - 2x - 8
3. f(x) = x³ - 3x² - 10x + 24

Write a polynomial function with the given factors.

4. (x + 3), (x - 7), (x - 1), and (x + 2)
5. (x + 6), (x - 3), and (x + 1)
6. (x + (3)) and (x + 1)

1. i
2. (2); -4
3. -3; 2; -4
4. f(x) = x³ - 5x² - 17x +21
5. f(x) = x³ - 2x² - 21x - 18
6. f(x) = x³ - 2x² - 3x - 6