Zero (or null) polynomial

Here you will find what a zero polynomial is, also known as a null polynomial, and you will see examples of this type of polynomial.

What is a zero (or null) polynomial?

The definition of zero or null polynomial is as follows:

In mathematics, the zero polynomial, also called null polynomial, is a polynomial in which all its coefficients are equal to 0.

The corresponding polynomial function of the zero polynomial is the constant function with value 0.

Note that the zero of a polynomial is a totally different concept. You can see what the zero of a polynomial is and how to calculate it in the following link:

Zero of a polynomial

Examples of zero (or null) polynomials

Once we have seen the meaning of a null (or zero) polynomial, let’s now look at several examples of this type of polynomial:

  •  P(x)=0
  •  Q(x)=0x+0
  •  R(x)=0x^2+0x+0
  •  S(x)=0x^3+0x^2+0x+0

One of the properties of null or zero polynomials is that they are the additive identity of the additive group of polynomials, that is, when we add any polynomial with the zero polynomial we obtain the same polynomial as a result.

P(x)+0=P(x)

➤ See: how to add polynomials

One may think that the degree of the zero or null polynomial is 0. However, in mathematics the zero polynomial is considered to have degree -1. And yes, it’s weird, but it actually makes sense. Discover the reason for this so curious in the following link:

➤ See: degree of a polynomial

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