Advanced Algebra

The Fundamental Theorem of Algebra:
If f(x) is a polynomial of degree n where n > 0, then the equation f(x)=0 has at least one solution in the set of complex numbers

Corollary:
If f(x) is a polynomial of degree n where n > 0, then the equation f(x)=0 has exactly n solutions provided each solution repeated twice is counted as two solutions, each solution repeated three times is counted as three solutions, and so on.

a + bi and a – bi are complex conjugates. If a + bi is an imaginary zero of f(x), then a – bi is also a 0

Zero: k is a zero of the polynomial function f(x), find by setting f(x)=0

Factor: x – k is a factor of the polynomial f(x)

Solution: k is a solution (or root) of the polynomial equation f(x) = 0

Tendency: What the function is doing
There are 3 tendencies up, down, and no change

Extreme Point:
The minimum value (min) OR Maximum value (max)
Each function has it’s own min and max, even if it is a part of a bigger function
Min and max is only ONE value but can be MULTIPLE points

2α

Local: characteristics for that ONE specific function

Global: characteristics for the entire big function AKA piecewise function