Polynomials Vocab

Binomial Theorem

• The formula for finding any power of a binomial without multiplying at length.
• describes the algebraic expansion of powers of a binomial

Combinations

• A formula that contains many different variables.

Conjugates

• a conjugate is a binomial formed by negating the second term of a binomial

Factor Theorem

• the factor theorem is a theorem linking factors and zeros of a polynomial
• It is a special case of the polynomial remainder theorem
• he factor theorem states that a polynomial has a factor if it is a root

Fundamental Theorem in Algebra

• every non-constant single-variable polynomial with complex coefficients has at least one complex root.

Imaginary Root Theorem

• roots are complex when the discriminant is negative.
• if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.

Irrational Root Theorem

• According to the rational root theorem, if the root is rational, then it should be either 1 or -1. It isn't. If the root is irrational, then its conjugate

Multiplicity

• the multiplicity of a member of a multiset is the number of times it appears in the multiset.
• number of times a given polynomial equation has a root at a given point.

Pascals Triangle

• Each number is the numbers directly above it added together.
• ex: 3 over 1 is 4

Polynomial Function

• A quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of x are all examples of polynomial functions

Rational Root Theorem

• a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials
• provides a complete list of possible rational roots of the polynomial equation anxn + an–1xn–1 + ··· + a2x2 + a1x + a0 = 0 where all coefficients are integers

Remainder Theorem

• the division of a polynomial by a linear polynomial is equal to
• used to determine the factors of polynomials and their remainders when divided by linear expressions

Synthetic Division

• a shorthand, or shortcut
• method of polynomial division in the special case of dividing by a linear factor