Degree Of A Polynomial

What is 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:

\(6x^{4} + 2x^{3}+ 3\)

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Degree of a Polynomial

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

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What is the degree of a polynomial?

For Example:

\(6x^{4} + 2x^{3}+ 3\)

The degree of Polynomial is 4.

Let’s take another example:

\(3x^{8}+ 4x^{3} + 9x + 1\)

The degree of Polynomial is 8.

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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 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)= \(6x^{0}\)

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 :\(5x^5 + 7 x^3 + 2x^5 + 3x^2 + 5+ 8x + 4\)

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

\((5x^5 + 2x^5) + 7 x^3 + 3x^2+ 8x + (5 +4) \)

2. Ignore all the coefficients

\( x^5  + x^3 + x^2 + x + x^{0} \)

3. Arrange the variable in descending order of their powers

\( x^5  + x^3 + x^2 + x + x^{0} \)

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

deg(\( x^5  + x^3 + x^2 + x + x^{0} \))) = 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.


Practise This Question

Front view of the above shown solid figure is__________.