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In mathematics, a polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, combined using addition, subtraction, and multiplication operations. The variables in a polynomial are usually raised to nonnegative integer powers. Here’s a general form of a polynomial:
P(x) = a_nx^n + a_{n1}x^{n1} + … + a_2x^2 + a_1x + a_0
In this expression, P(x) represents the polynomial, x is the variable, and a_n, a_{n1}, …, a_2, a_1, a_0 are the coefficients. The exponent on each term, represented by n, is a nonnegative integer, and it determines the degree of the polynomial.
Polynomials can have multiple terms, and the terms are typically written in decreasing order of their exponents. For example, a quadratic polynomial has a degree of 2, a cubic polynomial has a degree of 3, and so on.
Polynomials are widely used in various areas of mathematics, engineering, physics, and computer science. They play a fundamental role in algebra, calculus, and numerical analysis, and they are used to model and solve a wide range of realworld problems.