Chapter 5 Polynomials

factored completely

polynomial is written as a product of unfactorable polynomials with integer coefficients

end behavior

the behavior of the graph of a function as x approaches positive infinity or negative infinity

leading coefficient

the coefficient in the term of a polynomial function that has the greatest exponent

quadratic form

the form au² + bu + c, where u is any expression in x

standard form of a polynomial function

the form of a polynomial function that has terms written in descending order of exponents from left to right

scientific notation

the representation of a number in the form c x 10^n where 1≤c<10 and n is an integer

local minimum

the smallest y-value within a specified interval

degree

the sum of the exponents of its variables

finite differences

when the x-values in a data set are equally spaced, the differences of consecutive y-values

constant

monomials that contain no variables

polynomial function

a function of the form... the exponents are all whole numbers, and the coefficients are all real numbers

synthetic division

a method that can be used to divide a polynomial by a binomial where the leading coefficient must be 1

polynomial long division

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

synthetic substitution

a method used to evaluate a polynomial function

polynomial

a monomial or a sum of monomials

factor by grouping

factor common monomials from pairs of terms, and then look for a common binomial factor

repeated solution

for the polynomial equation f(x) = 0, k is a...if and only if the factor x-k has an exponent greater than 1 when f(x) is factored completely

local maximum

largest y-value within a specified interval