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combination

any unordered selection of r objects from a set of n objects

complex conjugates

the complex numbers a+bi and a-bi

conjugates

numbered pairs of the form a+√b and a-√b

degree

the exponent in a term

degree of a polynomial

the largest degree of any term of a polynomial

difference of cubes

an expression of the form a³-b³

expand

done by multiplying a polynomial and writing the resulting polynomial in standard form

Factor Theorem

the expression x-a is a linear factor of a polynomial if and only if the value of a is a zero of the related polynomial function

Fundamental Theorem of Algebra

if P(x) is a polynomial of degree n≥1 with complex coefficients, then P(x)=0 has at least one complex root

Imaginary Root Theorem

if the imaginary number a+bi is a root of a polynomial equation with real coefficients then the conjugate a-Bi is also a root

Irrational Root Theorem

Let a and b be rational numbers and let √b be an irrational number. If a+√b is a root of a polynomial equation with rational coefficients, then the conjugate a-√b is also a root

multiple zero

if a linear factor in a polynomial is repeated, the zero related to that factor is this

multiplicity

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

n factorial

for any positive integer n, n(n-1) ×...×3×2×1.0!=1

Pascal's Triangle

a pattern for finding the coefficients of the terms of a binomial expansion

permutation

an arrangement of items in a particular order

polynomial

a monomial or the sum of monomials

relative maximum

the y-value of a point on the graph of a function that is higher than the nearby points of the graph

relative minimum

the y-value of a point on the graph of a function that is lower than the nearby points of the graph

Remainder Theorem

if a polynomial P(x) of degree n≥1 is divided by (x-a), where a is a constant, then the remainder is P(a)

standard form of a polynomial

this has the terms in descending order by degree

sum of cubes

an expression of the form a³+b³

synthetic division

a method of dividing polynomials in which you omit all variables and exponents and perform division on the list of coefficients. You also reverse the sign of the divisor so that you can add throughout the process, rather than subtrct