Polynomial Vocabulary

polynomial

A monomial or sum/difference of monomials

rational number

A number that can be written as a/b where a and b are integers, but b is not equal to 0.

irrational number

A number whose decimal form is nonterminating and nonrepeating. Irrational numbers cannot be written in the form a/b, where a and b are integers (b cannot be zero).

upperbound

When a number is substiuted and every answer is positive -means that there is no zero beyond that point

quotient

the answer to a division problem

4th difference

the change in the change in the change in the change of y related to the change in x in the t-table of a function

3rd difference

the change in the change in the change of y related to the change in x in the t-table of a function

2nd difference

the change in the change of y related to the change in x in the t-table of a function

1st difference

the change of y related to the change in x in the t-table of a function

divisor

the number (term) by which a dividend is divided

multiplicity

the number of times the related linear factor of a polynomial function is repeated in the factored form of the polynomial

remainder

the part of the dividend that is left over when the dividend is not evenly divisible by the divisor

synthetic division

the shortcut for long division of polynomials when dividing divisors of the form x - k

Root

the solution of a polynomial equation

imaginary number

the square root of a negative number

linear term

A term with a degree of one.

Remainder Theorem

If a polynomial f(x) is divided by x - k, the remainder is r = f(k)

leading coefficient

The coefficient of the term with the highest degree

zeros

The roots or x-intercepts of a polynomial function

polynomial function

a function that is represented by a polynomial equation

polynomial long division

a method used to divide polynomials similar to the way you divide numbers

dividend

a number (polynomial) to be divided by another number

lower bound

a number equal to or less than any other number in a given set

complex number

a number of the form a+bi where a and b are real numbers and i is the square root of -1

Fundamental Theorem of Algebra

an nth degree polynomial has n solution(s), real or complex

Rational Root Theorem

if P(x) is a polynomial function with integer coefficients which has a rational root h/k in lowest terms, then h must be a factor of the constant term of P(x), and k must be a factor of the leading coefficient of P(x).