Constant Polynomial

A constant polynomial in algebra is a polynomial whose degree is equal to zero. The standard form of denoting a constant polynomial is f(x) = k, where k is a real number. Its graph is a horizontal straight line parallel to the x-axis as the value of the constant polynomial f(x) = k remains the same irrespective of the change in the variable x. The domain of a constant polynomial is all real numbers whereas its range is a singleton set consisting of a real number.

In this article, we will discuss in detail the constant polynomial and its various properties and characteristics, its general form, domain, and range, and plot its graph. We will also go through various solved examples for a better understanding of the concept.

A constant polynomial is a function of form f(x) = c, where c is a real number, whose highest degree is zero. In simple words, we can say that a constant polynomial is a polynomial in algebra whose output value remains the same irrespective of the change in the input values. Some of the examples of a constant polynomial are:

• f(x) = 4
• g(x) = -10
• f(x) = 3.4
• h(x) = -1/2
• g(x) = π

A polynomial in algebra with degree zero is called a constant polynomial. We can call it a constant function as well. Any constant value function of form f(x) = k, where k is a real number, is a constant polynomial. It does not involve any variable and its value does change with the change in the input values. An interesting fact about a constant polynomial is that whatever the input value may be, we can determine the output value (which is a constant) without any calculations.

As discussed in the previous sections, the degree of a constant polynomial is equal to zero. Let us recall the meaning of the degree of a polynomial. The degree of a polynomial is the greatest power of the variable in the polynomial equation. Since there is no variable involved in a constant polynomial so it can be written as f(x) = k = kx⁰. Since the highest power of the variable x is 0 here, therefore we can say that the degree of a constant polynomial is equal to 0.

Now that we have understood the meaning of a constant polynomial, we know that its output value does not change with the change in the input value. So, it has a straight line graph parallel to the x-axis. Given below is a graph of a constant polynomial f(x) = 3. Whatever may be the value of x, the corresponding output value remains the same which is equal to 3.

So far we have discussed the constant polynomial, let us now discuss the differences and similarities between a constant polynomial and a zero polynomial on the basis of their properties. A zero polynomial is a special case of a constant polynomial.

Important Notes on Constant Polynomial

• A constant polynomial has a degree equal to zero.
• The slope of the constant polynomial graph is equal to 0.
• The value of the output remains the same irrespective of the change in the input value of a constant polynomial.

☛ Related Articles:

• Types of Polynomials
• Polynomial Functions
• Polynomial In Standard Form

What is a Constant Polynomial?

A polynomial in algebra with degree zero is called a constant polynomial. It is also known by the name constant function. The standard form of denoting a constant polynomial is f(x) = k, where k is a real number.

What is the Degree of Constant Polynomial?

The degree of a polynomial is the greatest power of the variable in the polynomial equation. Since there is no variable involved in a constant polynomial so it can be written as f(x) = k = kx⁰. Since the highest power of the variable x is 0 here, therefore we can say that the degree of a constant polynomial is equal to 0.

What is Non-Zero Constant Polynomial?

A Non-Zero Constant Polynomial is a constant polynomial of the form f(x) = k, where k is any real number except 0.

How Many Zeros Does a Constant Polynomial Have?

A polynomial function can have up to n number of zeros, where n is the degree of the polynomial. Since a constant polynomial has a degree equal to zero, therefore it has no zeros.

Is 5 a Constant Polynomial?

Yes, f(x) = 5 is a constant polynomial as the output value is always equal to 5 irrespective of the change in the input value.

Is Constant Polynomial the Same as Zero Polynomial?

We can say that a zero polynomial is a constant polynomial but not all constant polynomials are zero polynomials. For example, f(x) = 4 is a constant polynomial but not a zero polynomial.

What is the Difference Between a Constant Polynomial and Zero Polynomial?

A zero polynomial is an example of a constant polynomial whose form is given by, f(x) = 0. Here the output is a constant equal to 0. A constant polynomial has a form f(x) = k, where k can be any real number.