# What is the Remainder Theorem?

Polynomials can be defined as a type of expression used to represent or express different numbers for the different branches of mathematics. It is categorized into many types based on the variables of a polynomial. One of them is the ‘linear polynomial’. A polynomial that has the degree of 1 is regarded as a linear polynomial. The formula that is used to divide a normal polynomial with a linear polynomial to get an appropriate remainder is known as the remainder theorem. Whenever we divide two different types of polynomials, there is a high probability that we get a residue value. This value is known as the remainder. Let us assume, a polynomial a ( x ) has been divided by the polynomial which is linear i.e. b ( x ), then the remainder will be written as r = a( x ) where ‘r’ is the remainder. The remainder theorem enables us to calculate a question without carrying out the steps of the algorithm. In this article, we shall cover some interesting concepts such as: what is a polynomial, the types of polynomial, and some significant points to remember.

## What is a Polynomial?

There are various branches of mathematics such as calculus, trigonometry, geometry, and many more. One of them is algebra. The concept of polynomials comes under the category of algebraic geometry. It can be defined as the type of expression that is used to represent or express various types of numbers. Expression is the mathematical statement which does not include an equal ( = ) sign. In a polynomial expression, the exponents of the variables must be a whole number. Those numbers which do not include any type of integers and decimals are known as whole numbers. Some examples of whole numbers are 0, 1, 4, 6, 8, and so on. A polynomial expression consists of three terms i.e. ‘constant’, ‘variable’, and ‘coefficient’. For example, 3x.x + 5 is a polynomial where 5 is regarded as a ‘constant’, x is denoted as a ‘variable’, and 3 is the coefficient of the polynomial expression. We shall cover the types of polynomials in the next section.

## Different Types of Polynomials

As mentioned above, the type of expression that is used to represent or express various types of numbers is known as a polynomial. The following points mentioned below briefly analyze the types of polynomials.

- A type of polynomial that consists of a single term can be defined as a monomial. The examples of monomials are as follows: 4xy, 6y.y, and so on.
- A type of polynomial that consists of exactly two terms can be regarded as a binomial. The examples of binomials are as follows: x + 4, y.y + 3, and many more.
- Similarly, a type of polynomial which is inclusive of three terms is defined as a trinomial. For example, 2x + y – 5 etc.

There are various other types of polynomials that are categorized based on the degrees of a given polynomial. Some examples are as follows, linear polynomial, quadratic polynomial, cubic polynomial, and so on.

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