A polynomial is a mathematical expression consisting of one or more variables and constants, combined using the operations of addition, subtraction, multiplication, division and raising to a non-negative integer power. Polynomials appear in almost all areas of mathematics and science. They are used to model physical phenomena such as motion, sound propagation and electrical circuits. In economics they are often used to describe demand and supply curves. Polynomials are usually written in standard form where the terms are ordered by decreasing powers of the variable(s). For example: 3×2 – 2x + 4 is written as (3×2 – 2x + 4). The highest exponent on any given variable is called its degree. In this example, the degree is 2 because x appears with an exponent of 2. Any polynomial with a single variable can be expressed in factored form where the factors are multiplied together to give the original expression. For example: 3×2 – 6x + 9 = (3x – 3) (x – 3). Polynomials can be added, subtracted and multiplied together just like any other algebraic expressions; however division can be more difficult since there may not always exist a single factorization that satisfies both sides of an equation. Furthermore, if one attempts to divide by a polynomial that has multiple factors then it becomes very difficult or impossible to express the result as a single polynomial; this problem is known as synthetic division” or “long division”. Despite these challenges, polynomials remain useful in many fields due to their wide applicability and relative ease of manipulation compared to other forms of mathematical expression. Additionally their properties have been well studied which makes them an ideal tool for studying certain types of problems such as those involving curves or surfaces which have equations involving higher order terms than those found in linear equations.
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