In mathematics, you might have heard about the term variables and coefficients. When an algebraic expression is made up of variables and coefficients, it is termed polynomials. This term has been excavated from the words of Greek, where the word ‘poly’ signifies many and the term nominal signifies ‘terms’. We can perform various types of arithmetic operations such as multiplication, addition, and subtraction for a polynomial expression except for the division as it is not performed by a variable. In order to understand this topic in a better way, let us take the help of an example, ‘4x.x + x + 5’, which consists of three terms. In this article, we will try to understand some basic concepts related to polynomials such as types and terms related to them and do a detailed analysis about them.
Degree of Polynomials
The highest or the greatest power present in the variable of a polynomial expression can be defined as the degree of polynomial. A polynomial is an algebraic expression that is made up of variables and coefficients. There are various types of degrees of polynomials such as the zero polynomial which signifies that all the coefficients will be equal to zero, the constant polynomial which basically means that the value of variables and coefficient will be the same throughout. There are other types as well such as the linear polynomial, the cubic polynomial, the quadratic polynomial, the quartic polynomial. This term is important in order to segregate an expression to be called homogeneous or not.
Types of Polynomial
On the basis of the terms, the polynomials are classified into three different types. The terms in a polynomial expression can be defined as the parts of an equation which is given by the positive sign (+), or negative sign (-). The following points mentioned below analyses the types of polynomials:
- Monomial: A polynomial expression that consists of only one term can be defined as the monomial. For any equation to be called a monomial, the term which is single should be a non-zero term. Let us take the help of an example in order to understand monomials in a better way; 4, 3x, -4xy, 4a are examples of a monomial polynomial.
- Binomial: A polynomial expression that consists of only two terms can be defined as the binomial polynomial. Whenever two or more monomials go under arithmetic operation such as subtraction or addition, the resultant value comes as a binomial.
- Trinomial: A polynomial expression that contains only three terms. Let us take the help of an example in order to understand trinomials in a better way; 3x.x + 6x + 8, 8b.b + 2x + 6 are the examples of trinomials.
Some Calculations Based on Polynomials
In the paragraph mentioned above, we dealt with the types of polynomial, the definition of polynomial, and the degree of a polynomial. In this paragraph, we will try to cover some calculations based on the polynomials so that you grasp the concept in a detailed manner. The following points mentioned below signify the calculations of polynomials:
Example 1: Find the value of X, if the given equation is 4x +2?
Given that,
Equation = 4x + 2
Let us now take the equation as = 0
Now, 4x + 2 = 0
4x = -2,
X = -2/4
X = -½.
Therefore, the value of x for the given equation is = -½.
Example 2: Find the value of Y, if the given equation is 3x +2?
Given that,
Equation = 3x + 2
Let us now take the equation as = 0
Now, 3x + 2 = 0
3x = -2,
X = -⅔.
Therefore, the value of x for the given equation is = -⅔.
If you want to learn about polynomials and their degrees of it in a detailed manner and in a fun way and interactive way, you may visit the Cuemath website.
