A type of algebraic expression that consists of variables and coefficients can be defined as the polynomial. An algebraic expression can be defined as the combination of the arithmetic operations such as addition, multiplication, and subtraction. Any quantity that can be counted or measured can be defined as a variable. Similarly, a coefficient can be considered as the value which is placed before a variable. The arithmetic operation of division cannot be implied in the polynomial expression. Any algebraic expression which contains polynomials can be regarded as the polynomial expression. The term ‘polynomials’ has been derived from Greek words which means ‘many terms’. It is segregated into two terms Poly which means many and nominal signifies terms. Some examples of polynomials are as follows: y.y + y – 12, 5x.x + 2y -7, and so on. In this article, we shall cover some topics related to polynomials such as the degree of a polynomial, types of polynomial, and so on.
Table of Contents
Degree of a Polynomial
We have already discussed the polynomial expression. The highest power in a variable in a polynomial expression can be defined as the degree of a polynomial. The degree of a polynomial has been classified into various types. One of them is the degree of a zero polynomial. A type of polynomial expression where the coefficients in the expression are equivalent to zero. The power is either not defined or written as -1. To recall, a coefficient can be considered as the value which is placed before a variable. A type of degree of a polynomial where the value remains constant can be defined as the degree of a constant polynomial. For the degree of 2, 3, and 4, the polynomial is defined as the quadratic, cubic, and quartic polynomials respectively. We shall cover the types of polynomials in the next section.
Types of Polynomial
As mentioned above, a type of algebraic expression which consists of variables and coefficients can be defined as the polynomial. There are three types of polynomials which are written as, monomial, binomial and trinomial. The following points mentioned below analyze these types of polynomials in a detailed manner.
- A type of polynomial expression that consists of only one term can be defined as the monomial. In a monomial, the value of the single term is equal to zero. Some examples of the monomial are as follows, 5x, 4, 3, and so on.
- A type of polynomial expression that consists exactly of two terms can be defined as binomial. The binomial can also be defined as the sum or difference of two or more monomials. Some examples of binomials are as follows, -5x + 3, 4x + 2, and so on.
- A type of polynomial expression that consists of three terms can be defined as a trinomial. A few examples of trinomials are as follows, 4x.x + 5x +7, and so on.
Examples of the Degree of a Polynomial
To recall, the highest power in a variable in a polynomial expression can be defined as the degree of a polynomial. Let us solve some examples based on the degree of a polynomial so that you can grasp the concept. Some of them are listed below:
Example 1: Find the degree, leading coefficient, and constant of the given polynomial expression, 4x.x.x + 2x + 3.
Solution: Given that,
Polynomial expression = 4x.x.x + 2x + 3.
The highest power of the variable is = 3.
Thus, the degree of the given polynomial is = 3.
The leading term of the polynomial = 4 as 4x.x.x.
The constant of the polynomial is = 3.
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