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).
