Alg 2 - Unit 5 - Polynomials

Polynomial Function

a function that is represented by a polynomial equation

Degree

the greatest exponent of any term in the polynomial

Constant

A term of degree of zero

Standard form of a polynomial

The form of a polynomial that places the terms in descending order by degree.

Leading Coefficient

The coefficient of the term with the highest degree

Quartic

a polynomial with a degree of 4

Quintic

a polynomial with a degree of 5

Long division of polynomials

A process of dividing polynomials that mirrors long division of numbers

Synthetic Division

a shorthand method of dividing by a linear binomial of the form (x-a) by writing only the coefficients of the polynomials

Rational Root Theorem

a theorem that provides a complete list of all possible rational roots of a polynomial equation

Irrational Conjugates Theorem

IRRATIONAL and IMAGINARY solutions will ALWAYS occur in pairs called CONJUGATES

Complex Conjugates Theorem

IRRATIONAL and IMAGINARY solutions will ALWAYS occur in pairs called CONJUGATES

“Uncomplete the Square”

To work backwards from the roots to determine the polynomial

PlySmlt2 APP

Application on the TI calculator that will solve polynomials

Even Multiplicity

When a function has at least 2 zeros (roots, solutions, x intercepts)

Odd Multiplicity

When a function has at least 3 zeros (roots, solutions, x intercepts)