What is a Polynomial Function?

Polynomial Functions are functions with many terms containing the constant, and variables with different positive exponents and coefficients.

It is generally represented by P(x). Polynomial functions have many terms as in polynomial, poly means many, and nominal means terms. The exponent of the polynomial function must be positive. The domain of the polynomial function is all the real numbers R.

Polynomial Function Definition

The generalized form of the polynomial function is defined as:

P(x) = a_nxⁿ + a_n-1x^n-1 + …… + a₂x² + a₁x + a₀

Where, 

• a_n, a_n-1, . . . a₂, a₁, a₀ are coefficients, 
• x is variable, and
• P(x) is the polynomial function in variable x.

The exponents of the variable should be the whole number. a_n, a_n-1,…… a₂, a₁, a₀ coefficients are real number constants. n is a positive number which is the degree of the polynomial. a_n is the leading coefficient as it is the coefficient of the degree of the polynomial. The leading coefficient in the polynomial function cannot be zero.

Degree of Polynomial Function

The degree of the polynomial function is the highest power of the variable in the function.

Example: Find the Degree of polynomial function P(x) that is given as follows:

P(x) = 4x³ + 3x² + 2x + 1

Solution:

• Degree of term 4x³ is 3, 
• Degree of term 3x² is 2,
• Degree of term 2x is 1, and
• Degree of term 1 is 0.

As the highest degree in all the terms is 3. 

Thus, the degree of the above polynomial function P(x) is 3.

Learn more about the Degree of Polynomials 

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.