1. The Fundamental Theorem of Algebra
(simplified)

2. Warm-Up Challenge The number is less than 1000.
The sum of the digits is 16.
The sum of the first digit and the last digit is 11.
The second digit is 3 more than the first.
What’s my number?
Answer: 259

3. 1. The Fundamental Theorem oF Algebra
A polynomial of degree n has exactly n roots when counting multiple roots and non-real solutions. How many roots? f(x) = 5x7 – 4x3 + 3x – 9 7 f(x) = -5x3 + 2x4 – x

4. 2. Solve
a) x3 – 8x2 + 25x – 26 = 0 Answer: x = 2, x = 3 + 2i, x = 3 – 2i b) x4 – 4x3 – 2x2 + 20x – 15 = 0 Answer: x = 1, x = 3, x = √5, x = -√5

5. 3. Write an equation with the given roots
Answer: f(x) = x3 + 3x2 – 10x
b) ± 3 , ± 6i
Answer: f(x) = x4 + 33x2 – 108

6. 4. If this is a 6th degree polynomial, describe the roots.