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Space Race
Defend Earth from alien invaders
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

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