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Polynomials are usually classified on the basis of their degree and the number of terms in the expression. The degree of a polynomial is the highest power of the variable in the equation given. It determines the behavior and the shape of the graph plotted for the polynomial given.
An example of a polynomial is :
f(x) = x²+2x-3
This polynomial has 3 terms in it.
Here, the degree of the polynomial is 2 since the term with the highest power of ‘x’ is ‘x²’, therefore, 2 is the highest power hence the degree of the polynomial as well.
This article will discuss different Types of Polynomials. Read the complete article for a better understanding of the types of polynomials.
Introduction to Polynomials
Polynomials are defined as the type of algebraic expressions whose variables have only non-negative integers as their powers.
For example:
f(x) 5x² – x + 1 is a polynomial.
The algebraic expression 3x³ + 4x + 5/x + 6x³/² is not a polynomial, since one of the powers of ‘x’ is a fraction and the other is negative.
To know more about polynomials, check: Polynomials
Types of Polynomials
As previously mentioned, the polynomials can be classified in two ways:
- On the basis of the degree
- On the basis of the number of terms.
The types of polynomials on the basis of degree are zero polynomial, linear, quadratic, and cubic polynomials.
The types of polynomials on the basis of the number of terms: monomials, binomials, trinomials, etc.
Types of Polynomials on the Basis of Degree
The power of the leading term is called the degree of the polynomial. It is also defined as the highest power of the variable. The degree of the Polynomials is obtained by arranging all the terms of polynomials in the descending order of their powers.
On the basis of the degree of the polynomial, the polynomials can be classified into 4 major types. The names are mentioned below.
- Zero or constant polynomial
- Linear polynomial
- Quadratic polynomial
- Cubic polynomial
The below-mentioned table provides a clear explanation of the above-mentioned types of Polynomials.
| Type of Polynomials | Definition | Example |
| Zero or Constant Polynomial | Polynomials with 0 degrees. | 3x⁰, 8y⁰, 4z⁰ |
| Linear Polynomial | Polynomials with 1 as the highest degree. | 5x, 9y, 10x – 3y |
| Quadratic Polynomial | Polynomials with 2 as the highest degree. | 3x², 7x²-4y+7 |
| Cubic Polynomial | Polynomials with 3 as the highest degree. | 8x³, 9x³-6x²+4x-2 |
Types of Polynomials on the Basis of Terms
There is a division of polynomials with respect to the number of terms present in their respective expression. There are polynomials with one term, two terms, three terms, and even more. Based on the number of terms, the polynomials are classified as:
Monomials
A monomial is a polynomial expression consisting of only a single term.
For example: 4t, 21x, 2y, 9pq.
Furthermore, 2x + 8x + 1x is a monomial because these are like terms added together, resulting in 11x, a single term.
Binomials
A binomial is a polynomial expression with two, unlike terms.
For example: 7x + x² is a binomial as it contains two unlike terms, that is, 7x and x².
Trinomials
A trinomial is a polynomial expression with three, unlike terms.
For example: 6x + 9x² – 12x³
Polynomial expressions with more than 3 terms also exist. Polynomials that have 4, unlike terms, are called four-term polynomials.
Similarly, polynomial expressions with 5 terms are called five-term polynomials, and so on.
Special Types of Polynomials
Apart from the above-mentioned types of polynomials, some special types exist simultaneously.
Monic polynomial
A polynomial expression whose leading coefficient is 1.
Example: x³ + 3x + 3.
Irreducible polynomial
A polynomial that cannot be further factored into a lower-degree polynomial.
Example: x² + 2 is an irreducible polynomial.
Homogeneous polynomial
A polynomial expression whose all the terms have the same degree.
Example: x² + xy + y².
FAQs on Types of Polynomials
What is a Polynomial?
A polynomial is an expression consisting of variables (or indeterminate), exponents, and constants. For example, 3x2 -2x-10 is a polynomial.
What are a polynomial's terms, degrees, and exponents?
If 2x2 – 3x +19 is a polynomial, then; Terms: 2x2,-3x & 19 Degree: 2 (the highest exponent of variable x) Exponents: Power raised to variable x, i.e. 2 and 1.
What is the standard form of the polynomial?
A standard polynomial is one where the highest degree is the first term; subsequently, the other terms come. For example, x3 – 3x2 + x -12 is a standard polynomial. So the highest degree in the given polynomial expression is 3, then comes 2, and then 1.
Is 6 a polynomial?
6 can be written as 6x0 or 0x2+0x+6, representing the polynomial expression. Therefore, we can consider 6 as a polynomial.
