Polynomials are mathematical expressions made up of variables and constants that can be added, subtracted, multiplied, and divided. They are used in business and science to create models and analyze physical phenomena. Polynomials can be organized into terms and used in equations to find variable values. Graphs of polynomial functions can vary in shape and provide visual representations of the function. Multivariate polynomials involve more than one variable and are more complex. Polynomials are an integral part of modern mathematics and used in various fields.
A polynomial is a mathematical expression of finite length. It is composed of both variables and constants. These variables and constants can be added, subtracted, multiplied and divided. They can also be raised to exponents, as long as those exponents are integers.
In mathematics and science, polynomials are extremely important. They are used to create sales models in business and to model physical phenomena in physics and chemistry. Polynomial functions also form the basis for much of the computation; derivatives and integrals of polynomial functions provide information to scientists, economists, physicians, and others about rates of change.
Polynomials take the form anxn+…+a2x2+a1x+a0, and are organized in terms, sometimes called monomials. A term is a section of a polynomial that is multiplied together and is typically composed of a constant multiplied by an exponent that is raised to a power. For example, 3×2 is one term and 3×2+2x+5 is a polynomial made up of three terms. Terms are sorted from highest to lowest by rank, the number of the exponent on a variable.
As many high schoolers learn, polynomials are often used in equations, where two polynomials are equal to each other. Typically, the goal of a polynomial equation is to find the value or values of the variable or variables. Solving these equations can provide information such as time or distance in practical physics-related scenarios.
Graphs are often used in the study of polynomial functions, which take the form of f(x)= anxn+…+a2x2+a1x+a0. The value of the variable, x, determines the value of the function as a whole, f(x). Graphs of polynomial functions can vary in shape from parabolas to intricate series of curves depending on the degree and complexity of the function. Such visual representations make it much easier to understand the meaning of the function, as they plot all values of f(x) based on the values of x in a given interval.
Multivariate polynomials involve more than one variable. They can involve any number of variables and generally become more complex as the number increases. Generally, little attention is paid to multivariate polynomials in high school. They are usually presented in upper-level college calculus classes dealing with three-dimensional shapes or the analysis of many different forms of combined data.
Polynomials have been used for a long time and are an integral part of modern mathematics. Their many forms lay the foundation for the representation of countless models in business, science, economics and other fields.
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