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Polynomials and Polynomial Functions

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PRESENTATION OUTLINE

Polynomials and Polynomial Functions

Binomial Theorem

A formula for finding any power of a binomial without multiplying a length

Combination

A way of selecting items from a collection the order selection does not matter

Conjugates

Number pairs of the form a+b and a-b are conjugates

Factor Theorem

A theorem linking factors and 0's of a polynomial .

Fundamental Theorem of Algebra

If P(x) is a polynomial of degree n>1 w/ complex coefficients then P(x)=0 has at least 1 complex root  

Imaginary Number

A complex # that can be written as a real #

Irrational Root Theorem

a and b are rational #'s and b is an irrational #.

Multiplicity

How many times a particular # is a zero for a given polynomial. 

Pascal's Triangle

Triangle of #'s where each # is the 2 #'s above it added together (except the sides)

Polynomial Function

Expression that has constants, variables, & exponents & are combined with  -, +, /. or *

Rational Root Theorem

A theorem providing complete list of possible rational roots of the polynomial expression  

Remainder Theorem

Divide a polynomial f(x) x-c you get f(x)= (x-c)*q (x)+r(x)

Standard Form of a Ploynomial

Putting terms of highest degree first to the smallest degree

Synthetic Division

A method of dividing polynomials to omit all variables & exponents