Degree of a Polynomial

A polynomial is defined as an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). It is a linear combination of monomials.

For Example:

6x4 + 2x3+ 3

What is the Degree of a Polynomial?

It is the highest or the greatest degree of a variable in the polynomial equations. It indicates the highest exponential power in the polynomial(ignoring the coefficients).

For Example:

6x4 + 2x3+ 3

The degree of Polynomial is 4.

Let’s take another example:

3x8+ 4x3 + 9x + 1

The degree of Polynomial is 8.

Degree of a Zero Polynomial

A Zero Polynomial is the one where all the coefficients are equal to zero.

The degree of the zero polynomial is either undefined, or it is set equal to -1.

Degree of a Constant Polynomial

A constant polynomial is that whose value remains the same. It contains no variables.

The example for this is:

P(x)=c.

Since there is no exponent so no power to it.

Thus, the power of the constant polynomial is Zero.

Any constant can be written with a variable with the exponential power of zero.

Constant term = 6

Polynomial form P(x)= 6x0

How to Find the Degree of a Polynomial?

A Polynomial is merging of variables assigned with exponential powers and coefficients.

The steps to find the degree of a polynomial are as follows:-

For example if the expression is :5x5 + 7 x3 + 2x5+ 3x2+ 5+ 8x + 4

1. Combine all the like terms that is the terms with the variable terms.

\((5x5+ 2x5) + 7 x3+ 3x2+ 8x + (5 +4)

2. Ignore all the coefficients

 x5+ x3+ x2+ x1 + x0

3. Arrange the variable in descending order of their powers

 x5+ x3+ x2+ x1 + x0

4. The largest power of the variable is the degree of the polynomial

deg( x5+ x3+ x2+ x1 + x0) = 5

Every polynomial with a specific degree has been assigned a specific name as follows:-

Degree 0 – Constant

Degree 1 – Linear

Degree 2 – Quadratic

Degree 3 – Cubic

Degree 4 – Quartic

and so on.

Degree of a polynomial Examples

Some of the examples of the polynomial with its degree are:

  • 5x5+4x2-4x+ 3 – The degree of the polynomial is 5
  • 12x-5x2 + 2 – The degree of the polynomial is 3
  • 4x +12 – The degree of the polynomial is 1
  • 6 – The degree of the polynomial is 0

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