polynomial (redirected from Polynomials)

polynomial, mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a₀xⁿ+a₁xⁿ⁻¹+a₂xⁿ⁻²+…+a_n−1x+a_n where n is a positive integer and a₀, a₁, a₂, … , a_n are any numbers. An example of a polynomial in one variable is 11x⁴−3x³+7x²+x−8. The degree of a polynomial in one variable is the highest power of the variable appearing with a nonzero coefficient; in the example given above, the degree is 4.

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polynomial

In algebra, an expression consisting of numbers and variables grouped according to certain patterns. Specifically, polynomials are sums of monomials of the form axⁿ, where a (the coefficient) can be any real number and n (the degree) must be a whole number. A polynomial's degree is that of its monomial of highest degree. Like whole numbers, polynomials may be prime or factorable into products of primes. They may contain any number of variables, provided that the power of each variable is a nonnegative integer. They are the basis of algebraic equation solving. Setting a polynomial equal to zero results in a polynomial equation; equating it to a variable results in a polynomial function, a particularly useful tool in modeling physical situations. Polynomial equations and functions can be analyzed completely by methods of algebra and calculus. See also orthoganal polynomial.

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polynomial

1. 

a. a mathematical expression consisting of a sum of terms each of which is the product of a constant and one or more variables raised to a positive or zero integral power. For one variable, x, the general form is given by: a₀xⁿ + a₁x^n--1 + … + a_n--1 x + a_n, where a₀, a₁, etc., are real numbers

b. any mathematical expression consisting of the sum of a number of terms

2. Biology a taxonomic name consisting of more than two terms, such as Parus major minor in which minor designates the subspecies

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1.	(mathematics)	polynomial - An arithmetic expression composed by summing multiples of powers of some variable. P(x) = sum a_i x^i for i = 0 .. N The multipliers, a_i, are known as "coefficients" and N, the highest power of x with a non-zero coefficient, is known as the "degree" of the polynomial. If N=0 then P(x) is constant, if N=1, P(x) is linear in x. N=2 gives a "quadratic" and N=3, a "cubic".
2.	(complexity)	polynomial - polynomial-time.