Polynomial

In mathematics, a polynomial is a kind of mathematical expression. It is a sum of several mathematical terms called monomials. That is, a number, a variable, or a product of a number and several variables. When an algebraic expression contains letters mixed with numbers and arithmetic, like ${\displaystyle 7x^{4}(-3)x^{3}+19x^{2}(-8)x+197}$, there is a good chance that it is a polynomial. Polynomials are taught in algebra, which is a gateway course to all technical subjects. Mathematicians, scientists and engineers all use polynomials to solve problems.

In algebra, when letters, numbers, and arithmetic symbols occur together, the understanding is that the letters stand for variables, which are either symbols of their own, numbers not yet known, or numbers that change during the course of the problem (such as time). A polynomial is an algebraic expression in which the only arithmetic is addition, subtraction, multiplication and whole number exponentiation. If harder operations are used, such as division or square roots, then this algebraic expression is not a polynomial. Polynomials are often easier to use than other algebraic expressions.

Polynomials are often used to form polynomial equations, such as the equation ${\displaystyle 7x^{4}(-3)x^{3}+19x^{2}(-8)x+197=0}$, or polynomial functions, such as ${\displaystyle f(x)=7x^{4}(-3)x^{3}+19x^{2}(-8)x+197}$.