math vocab chapter 3

degree of a polynomial

the greatest power of the variable in the expression determined by the highest exponent among its term with non-zero coefficients

leading coefficient

the coefficients of the greatest power of x

polynomial function

a monomial or the sum of two monomials

relative maximum

a point where the function has the greatest value over its interval, usually at a turning point

relative minimum

a point where the function has the least value over its interval, usually at a turning point

standard form of a polynomial

lists the terms by degree in descending numerical order. For each degree, all like terms must be combined

turning point

points where the function values change from increasing to decreasing or vice-versa

binomial theorem

a mathematical formula that provides a way to expand a binomial expression raised to any power expressed as (a+b)ⁿ. The expansion is the sum of terms calculated using binomial coefficients, which represent the number of ways to choose a certain number of items from a set. The formula for each term involves the terms a and b raised to specific powers and a binomial coefficient.

identity

an equation between two polynomial expressions in which one side can be transformed into the other side using defined rules of caluculation

pascal’s triangle

the triangular pattern of numbers where each number is the sum of the two numbers diagnally above it

factor theorem

state the expression x-a is a factor of a polynomial p(x) if and only if p(a)=0

remainder theorem

states that if a polynomial p(x) is divided by x-a, the remainder is p(a)

synthetic division

a method is used to divide a polynomial by a linear expression in the form of x-a. Note that the leading coefficient of the divisor is 1, and that a is the zero of the divisor

mulitplicity of a zero

the number of items its related factor appears in the factored form of the polynomial

even function

when a function is symmetric about the y-axis

odd function

when a function is symmetric about the origin