Polynomials: Definitions, Degrees And Applications In Mathematics And Real-World Scenarios

Polynomial

An algebraic expression that is the sum of one or more terms (or monomials)

A polynomial is a mathematical expression consisting of variables and coefficients, where the variables only have non-negative integer exponents. In other words, a polynomial is a function that is defined as a sum of monomials (terms), where each monomial is a product of a coefficient and one or more variables raised to non-negative integer exponents. For example, consider the polynomial f(x) = 3x^2 – 5x + 7. This polynomial has variables x, with exponents 2 and 1, and coefficients 3, -5, and 7.

A polynomial can be of different degrees, depending on the highest exponent of the variables in the polynomial. For example, the polynomial f(x) = 3x^2 – 5x + 7 is a quadratic polynomial of degree 2, because the highest exponent of the variable x is 2.

Polynomials are often used to model mathematical and real-world problems. They have many important properties such as the leading coefficient test, the intermediate value theorem, and the fundamental theorem of algebra. They are also widely used in calculus and other branches of mathematics for their analytic and algebraic properties.

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