Types of Polynomials
Polynomials can be classified in two ways: based on degree and based on the number of terms.
- The types of polynomials based on the degree are zero polynomial, linear, quadratic, and cubic polynomials.
- The types of polynomials based on the number of terms are monomials, binomials, trinomials, etc.
Let us see each of these types in the upcoming sections in detail.
🔴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 3x0 |
| 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. | 8x2 + 7y – 9, m2 + mn – 6 |
| Cubic polynomial | Polynomials with 3 as the degree of the polynomial are called cubic polynomials. | 3x3,p3 + 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 + 4x2 is a binomial as it contains two unlike terms, that is, 3x and 4x2. and 10pq + 13p2.
- Trinomials: A trinomial is a polynomial with three, unlike terms. For example, 3x + 5x2 – 6x3 and 12pq + 4x2 – 10.
We can also have more than 3 terms in a polynomial expression. Polynomials that have 4, unlike terms are called four-term polynomials. Similarly, polynomials with 5 terms are called five-term polynomials, and so on.
🔷Important Notes on Types of Polynomials:
- 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, 2/(x+2) is not a polynomial.
let’s practice!
