Chapter 6 vocab algebra 2

polynomial long division

A method used to divide polynomials similar to the way you divide numbers.

synthetic division

a method used to divide a polynomial by an expression of the form x-k.

polynomial function

function written in the form f(x)=anxn+an-1xn-1+...+a1x+a0. an does not equal zero, the exponents are all real numbers, and the coefficients are all real numbers. an is the leading coefficient, a0 is the constant term, and n is the degree.

fundamental theorem of algebra

if f(x) is a polynomial of degree n where n>0, then the equation f(x)=0 has at least one root in the set of complex numbers.

rational zero theorem

if f(x)=anxn+...+a1x+a0 has integer coefficients, then every rational zero of f has the following form: p/q=factor of constant term a0/ factor of leading coefficient an.

end behavior

the behavior of the graph as x approaches positive infinity or negative infinity.

finite differences

the first- order differences of a polynomial function f(x) are found by subtracting function values for equally spaced x values. The second order differences are found by subtracting consecutive first-order differences. The third- order differences are found by subtracting consecutive second-order differences, etc.

local maximum

the y-coordinate of a turning point of the graph of a function if the point is higher than all nearby points.

local minimum

the y-coordinate of a turning point of the graph of a function if the point is lower than all nearby points.