Types of Polynomials
In algebra, a polynomial is an expression that is made up of variables and constants in which the exponents of the variables are only positive integers and not fractions. The polynomial terms are separated mostly by either addition or subtraction operators. Polynomials find their applications in writing polynomial equations and defining polynomial functions. An example of a polynomial expression is x^{2}+2x3. This polynomial has a degree of 2 since the term with the highest power of 'x' is 'x^{2}'. This polynomial has 3 terms. Polynomials can be categorized with respect to their total number of terms and their degree.
Polynomials Definition
Polynomials are algebraic expressions in which the variables have only nonnegative integer powers. For example,: 5x^{2 } x + 1 is a polynomial. The algebraic expression 3x^{3 }+ 4x + 5/x + 6x^{3/2 }is not a polynomial, since one of the powers of 'x' is a fraction and the other is negative. Polynomials are expressions with one or more terms having a nonzero coefficient. The terms comprise variables, exponents, and constants. The first term of the polynomial is called the leading term. A standard polynomial is one where the highest degree is the first term, and the subsequent terms are arranged in descending order of the powers or the exponents of the variables followed by constant values. The number multiplied with a variable is called the coefficient. The number without any variable is called a constant.
Types of Polynomials Based on Degree
The power of the leading term or the highest power of the variable is called the degree of the polynomial. This is obtained by arranging the polynomial terms in the descending order of their powers. Based on the degree of the polynomial, they can be classified into 4 major types. They are,
 Zero or Constant polynomial
 Linear polynomial
 Quadratic polynomial
 Cubic polynomial
Look at the table given below to understand the meaning of the types of polynomials with examples.
Type of Polynomial  Meaning  Examples 

Zero or constant polynomial  Polynomials with 0 degrees are called zero polynomials.  3 or 3x^{0} 
Linear polynomial  Polynomials with 1 as the degree of the polynomial are called linear polynomials. In linear polynomials, the highest exponent of the variable(s) is 1  x + y  4, 5m + 7n, 2p 
Quadratic polynomial  Polynomials with 2 as the degree of the polynomial are called quadratic polynomials.  8x^{2} + 7y  9, m^{2} + mn  6 
Cubic polynomial  Polynomials with 3 as the degree of the polynomial are called cubic polynomials. 
3x^{3}, p^{3} + pq + 7 
Types of Polynomials Based on Terms
There are different types of polynomials with respect to their number of terms. There are polynomials with one term, two terms, three terms, and even more. Based on the number of terms, polynomials are classified as:
 Monomials: A monomial is a polynomial expression that contains only one term. For example 4t, 21x, 2y, 9pq. Furthermore, 2x + 5x + 10x is a monomial because these are like terms added together that result in 17x.
 Binomials: A binomial is a polynomial with two, unlike terms. For example, 3x + 4x^{2} is a binomial as it contains two unlike terms, that is, 3x and 4x^{2}. and 10pq + 13p^{2}.
 Trinomials: A trinomial is a polynomial with three, unlike terms. For example, 3x + 5x^{2} – 6x^{3} and 12pq + 4x^{2} – 10.
We can also have more than 3 terms in a polynomial expression. Polynomials that have 4 unlike terms are called fourterm polynomials. Similarly, polynomials with 5 terms are called fiveterm polynomials, and so on.
Important Notes
 In a polynomial, two terms are separated by the addition or subtraction sign. Multiplication and division operators are not used to create more terms in a polynomial. For example, 3xy is considered as 3 × x × y, is a monomial, whereas 3x+y is a binomial.
 Based on the terms in a polynomial, it can be classified into the following 3 types. They are monomial, binomial, trinomial.
 Based on the degree of a polynomial, it can be classified into 4 types. They are zero polynomial, linear polynomial, quadratic polynomial, cubic polynomial.
 Polynomials should have a whole number as the degree. Expressions with negative exponents are not polynomials. For example, x^{2} is not a polynomial.
 Polynomials do not have variables in their denominator. For example, \(\dfrac{2}{x+2}\) is not a polynomial.
Topics Related to Types of Polynomials
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Solved Examples on Types of Polynomials

Example 1: From the list of polynomials find the types of polynomials that have a degree of 2 and above 2 and name them.
i) x + 7
ii) x^{2} + 3x + 2
iii) z^{3} + 2xz + 4Solution:
The given polynomials are in the standard form. The degree of a polynomial is found by checking for the term with the greatest exponent. In the first polynomial, x^{2} + 3x + 2 the degree is 2, and so it is called a quadratic polynomial. In z^{3} + 2xz + 4, the polynomial has a degree of 3. It is called a cubic polynomial. These are the two polynomials with a degree or 2 and greater than 2.

Example 2: Classify the given polynomials.
i) n^{3} + 6
ii) 5x^{2} + 2xy + 1
iii) p  8^{2}
iv) 2p^{2} + q  11
v) 34Solution:
We classify the given polynomials with respect to their degree and the number of terms.
n^{3}+6 is a binomial cubic polynomial as the highest exponent (degree of polynomial) with the variable is 3 and there are 2 terms in the polynomial.
5x^{2}2xy+1 is a trinomial quadratic polynomial as the degree is 2 and there are 3 terms in the polynomial.
p8^{2 }is a binomial linear polynomial as the degree of the polynomial is 1 and there are 2 terms in the polynomial.
2p^{2}+q11 is a trinomial quadratic polynomial. The degree of the polynomial is 2 and there are 3 terms present in it.
34 is a monomial zero polynomial as the degree of the polynomial is 0 and there is a single term in the polynomial.
Practice Questions on Types of Polynomials
FAQs on Types of Polynomials
What are the Types of Polynomials?
A polynomial is an expression that is made up of variables and constants. Polynomials are categorized based on their degree and the number of terms. Based on the number of terms in a polynomial, there are 3 types of polynomials. They are monomial, binomial and trinomial. Based on the degree of a polynomial, they can be categorized as zero or constant polynomials, linear polynomials, quadratic polynomials, and cubic polynomials.
What are the Types of Polynomials Based on the Number of Terms?
Polynomials are categorized according to the number of terms as follows. They are,
 Monomials: A monomial is a polynomial expression that contains only one term. For example, 2x + 5x + 10x is a monomial because when we add the like terms it results in 17x. Furthermore, 4t, 21x, 2y, 9pq are also monomials.
 Binomials: A binomial is a polynomial with two, unlike terms. For example, 3x + 4x^{2} is a binomial as it contains two unlike terms, that is, 3x and 4x^{2}. Likewise, 10pq + 13p^{2} is also a binomial.
 Trinomials: A trinomial is a polynomial with three, unlike terms. For example, 3x + 5x^{2} – 6x^{3} is a trinomial. Likewise, 12pq + 4x^{2} – 10 is also a trinomial.
In a polynomial, there should not be any negative number as the exponent of the variable. The variable should not be in the denominator of the polynomial that is in fractional form.
What are the Types of Polynomials Based on Degree?
Polynomials can be classified on the basis of their degree as follows. They are,
 Zero or Constant polynomial: Polynomials with 0 degrees are called zero polynomials. For example, 2 or 2y^{0}.
 Linear polynomial: Polynomials with 1 as the degree of the polynomial are called linear polynomials. In linear polynomials, the highest exponent of the variable(s) is 1. For example, p + q  2.
 Quadratic polynomial: Polynomials with 2 as the degree of the polynomial are called quadratic polynomials. For example, 8x^{2} + 7xy + 3.
 Cubic polynomial: Polynomials with 3 as the degree of the polynomial are called cubic polynomials. For example. 3x^{3}  1.
What is a Polynomial with 5 Terms Called?
Polynomials with 5 terms are known as fiveterm polynomials. For example, 3x^{3}xy+y^{2}+6x^{2}8.What is a Polynomial with 4 Terms Called?
Polynomials with 4 terms are known as quadrinomials. For example, x^{3}+3x2y+5.visual curriculum