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Polynomials and Polynomial Functions Vocabulary

Published on Nov 20, 2015

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PRESENTATION OUTLINE

Polynomials and Polynomial Functions Vocabulary

By: Romyrl Mestiola

Binomial Theorem

- A general formula for expanding a binomial.

Combination

- A selection in which the order does not matter.

Conjugates

- Number pairs of the form a + square root of b and a - square root of b.

Factor Theorem

- States that, 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.

Fundamental Theorem of Algebra

-States that if P(x) is a polynomial of degree n is greater than or equal to 1 with complex coefficients, then P(x) = 0 has at least one complex root. 

Imaginary Root Theorem

-States that, if the imaginary number a + bi is a root of a polynomial equation with real coefficients, then the conjugate a - bi also is a root.

Irrational Root Theorem

-States that, Let a and b be rational numbers and the square root of b an irrational number.If a+the square root of b is a root of the polynomial equations,then the conjugate a-the square root of b is also a root.

Multiplicity

-The multiplicity of a member of a multiset is the number of times it appears in the multiset. 

Pascal's Triangle

- A triangle of numbers in which a row represents the coefficients of the binomial series.

Polynomial Function

- Has the form, where are real numbers and n is a nonnegative integer.

Rational Root Theorem

-Used to check whether a polynomial has rational roots (zeros).

Remainder Theorem

-The process of dividing a polynomial f(x) by a polynomial D(x) and finding the remainder.

Standard Form of a Polynomial

-When the terms of the polynomial are set up from the highest to the lowest. 

Synthetic Division

-A shorthand method of polynomial division in the special case of dividing by a linear factor and it only works in this case.