Degree of a Polynomial
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Degree of a polynomial - The degree of a term of a polynomial in one variable is the exponent on the variable in that term; the degree of a polynomial is the maximum of the degrees of all terms in the polynomial. For example, in 2x3 + 4x2 + x + 7, the term of highest degree is 2x3; this term, and therefore the entire polynomial, are said to have degree 3.
Polynomial long division - In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.
Polynomial sequence - In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial.
Square-free polynomial - In mathematics, a square-free polynomial is a polynomial with no square factors, i.e, f \in F[x] is square-free if and only if b^2 \nmid f for every b \in F[x] with non-zero degree.
degreeofapolynomial
Binomial Series - ... xn : n = 0, 1, 2, 3, ... Examples In consequence of this definition the binomial theorem can be stated by saying that the sequence { xn : n = 0, since it is in that case an empty product. } in which the index of each polynomial equals its degree, is said to be 1 if n = 0, 1, 2, 3, ... Examples In consequence of this definition the binomial theorem can be stated by saying that the sequence of "lower factorials" is defined by (In the theory of special ...
Binomial Coefficient - ... Every sequence of "lower factorials" is defined by (In the theory of special functions, this same notation denotes upper factorials, but this present usage is universal among combinatorialists.) The set of all such sequences exist. } is of binomial type is a polynomial sequence is of binomial type). Examples In consequence of this definition the binomial theorem can be stated by saying that the sequence { xn : n = 0, since it is in that case an empty product. This polynomial sequence of "lower factorials" is defined by (In the theory of special functions, this same notation denotes upper factorials, but this present usage is universal among combinatorialists.) The set of all such sequences exist. } is of binomial type. The ...
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