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combination

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

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complex conjugates

the complex numbers a+bi and a-bi

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conjugates

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

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degree

the exponent in a term

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degree of a polynomial

the largest degree of any term of a polynomial

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difference of cubes

an expression of the form a³-b³

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expand

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

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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

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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

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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

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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

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multiple zero

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

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multiplicity

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

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n factorial

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

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Pascal's Triangle

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

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permutation

an arrangement of items in a particular order

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polynomial

a monomial or the sum of monomials

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relative maximum

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

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relative minimum

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

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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)

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standard form of a polynomial

this has the terms in descending order by degree

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sum of cubes

an expression of the form a³+b³

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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

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