Types of Polynomial Functions
We can classify the polynomial functions based on various different parameters such as the number of terms it contains or their degree. Classification of polynomial functions based on these parameters is given below:
Based on the Number of Terms
Based on the Number of Terms, a polynomial Function can be classified as follows:
- Monomial
- Binomial
- Trinomial
- and so on …
Let’s learn about these types with their examples in detail as follows:
Monomial: Monomials are polynomial functions with only one term. Some examples of monomials are:
- f = 2xy
- g = 4a2
- h = -3b3c2
- etc.
Binomial: Binomials are polynomial functions with only two terms. Some examples of binomials are:
- f = 3x + 2y
- g = x2 + 2xy
- h = 4m2 – 6n
- etc.
Trinomial: Trinomials are polynomial functions with only three terms. Some examples of trinomials are:
- f = 2x + 3y – z
- g = x2 + 5xy – 2y2
- h = 3m3 + 2m2n – mn2
- etc.
Based on the Degree
Based on the degree of the given polynomial function we can classify the function into the following types:
- Constant Polynomial Function: The polynomial function with the degree zero i.e., only constant is called the constant polynomial function. It is of the form P(x) = a.
- Zero Polynomial Function: The polynomial function which is zero is called the zero-polynomial function. It is of the form P(x) = 0.
- Linear Polynomial Function: The polynomial function with the degree one is called the linear polynomial function. It is of the form P(x) = ax + b.
- Quadratic Polynomial Function: The polynomial function with degree two is called the quadratic polynomial function. It is of the form P(x) = ax2 + bx + c.
- Cubic Polynomial Function: The polynomial function with the degree three is called the cubic polynomial function. It is of the form P(x) = ax3 + bx2 + cx + d.
- Quartic Polynomial Function: The polynomial function with the degree one is called the quartic polynomial function. It is of the form P(x) = ax4 + bx3 + cx2 + dx + e.
Learn more about Types of Polynomials
Polynomial Functions
Polynomial Functions are functions consisting of many algebraic terms including constants, variables of different degrees, coefficients, and positive exponents. The degree of the polynomial function is the highest exponent of the variable.
In this article, we will learn about Polynomial Functions, their examples, the degree of polynomial functions, etc. We will also learn about the types of polynomial functions, their graphs, the roots of polynomial functions, and how to identify whether the function is a polynomial function or not.
Table of Content
- What is a Polynomial Function?
- Examples of Polynomial Function
- Types of Polynomial Functions
- Polynomial Functions Graphs
- Zeros of Polynomial Function
- How to Identify a Polynomial Function?
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