Constant Polynomial

A constant polynomial is an algebraic expression that contains only a constant term. The degree of a constant polynomial is zero if the constant is non-zero. For the zero polynomial \((f(x) = 0)\), the degree is usually considered undefined, though some conventions assign it a degree of 0. A constant polynomial is written as \(f(x) = k\), where k is a real number. For example, the constant polynomial \(f(x) = 7\) is represented on a graph as a horizontal line at y = 7. 

The constant polynomial is one where the highest power of the variable is zero. A constant polynomial has no variable term, which means the highest power of the variable is 0. The degree is the highest exponent of x with a non-zero coefficient; the degree of a constant polynomial is 0. The degree of a constant polynomial is zero if the constant is non-zero. If the constant is zero, its degree is undefined and it is called a zero polynomial.

As seen in the previous section a constant polynomial has the form \(f(x) = k\), where k is a real number (e.g., 2, 4, -6, 0.8) and no variable terms are present. In a constant polynomial, the graph appears as a horizontal line parallel to the x-axis, intersecting the y-axis at \(y = k\). 

The graph above shows the constant polynomial \(f(x) = 6\). No matter what the value of x is, the corresponding output is always 6.
 

Let’s compare the constant polynomials and zero polynomials of their properties, and see how they are different.
 

Constant polynomials may look simple, but they form the foundation for understanding higher-degree equations. Learning their properties helps build clarity in algebraic concepts.

• Remember that a constant polynomial has no variable it’s just a number like 5, −2, or 0.
  
   
• The degree of every non-zero constant polynomial is always 0.
  
   
• A zero polynomial (0) is a special case and has an undefined or no degree.
  
   
• Constant polynomials have the same value for all values of x they never change.
  
   
• Practice identifying constant terms in various polynomial equations to strengthen your understanding.

Polynomials play the main role in day-to-day life. Polynomials are used in various applications, like designing a bridge, computer graphics, and more. Here are some applications given below.

 Designing structures: Engineers use a polynomial to model how the bridge reacts to loads and strains. For example, engineers use polynomial equations to calculate how much a bridge beam bends under the weight of cars and trucks. This helps to handle the weight that the bridge is supposed to carry.

Computer graphics:  In computer graphics, the polynomials are used to create 3D objects and shapes. For example, a polynomial equation can help to describe how the surface of a car looks in a 3D movie or game, making it appear realistic and smooth.
 

Finance and economics: Polynomials are used by financial analysts to model the market patterns. For example, the polynomials can be used to check how a stock's price has changed over time. 
 

Projectile motion: A polynomial equation can model the path of a thrown ball, incorporating both its initial velocity and the constant downward pull of gravity. 
 

Image manipulation: Polynomials are used in digital image processing as they make the image bigger or smaller uniformly (keeping proportions the same) or non-uniformly (changing proportions).