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1.
complex conjugates: a+bi and a-bi

2.
conjugates: the expressions a+√b and a-√b where a and b are rational numbers

3.
difference of cubes: a3-b3=(a-b)(a2+ab+b2)

4.
Factor Theorem: The expression x - a is a linear factor of a polynomial if and only if the value a is a zero of the related polynomial function.

5.
Fundamental Theorem of Algebra: states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. Equivalently, the field of complex numbers is algebraically closed.

6.
Imaginary Root Theorem: if the imaginary number a+bi is a root of a polynomial equation with real coefficients then the conjugate a-Bi is also a root

7.
Irrational Root Theorem: Let a and b be rational numbers and let √b be an irrational number. If a + √b is a root of a polynomial equation with rational coefficients, then the conjugate a - √b also is a root.

8.
multiple zero: a repeated zero of a polynomial

9.
multiplicity: state of being various or manifold; a great number

10.
Rational Root Theorem: let p(x)=anxn+an-1xn-1+...+a1x+a0 be a polynomial with integer coefficients. then there are a limited number of possible roots p(x)=0

11.
relative maximum: point when the graph goes from increasing to decreasing

12.
relative minimum: The value of the function at a down-to-up turning point.

13.
sum of cubes: a3+b3=(a+b)(a2-ab+b2)

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