Degree of Polynomial

The degree of polynomial is the greatest exponent of a term. The greatest exponent should have a non-zero coefficient in a polynomial expressed as a sum or difference of terms which is commonly known as Canonical form. The sum of the powers of all variables in the term is the degree of the polynomial. The degree can also be specified as order. The degree of polynomial is for the single variable or the combination of two or more variables with the powers.

According to the degree of polynomials the names are assigned. Below listed are the degree of polynomials:

• The name of the zero degree polynomial is constant.
• The name of the 1 degree polynomial is linear.
• The name of the 2 degree polynomial is quadratic.
• The name of the 3 degree polynomial is cubic.
• The name of the 4 degree polynomial is quartic
• The name of the 5 degree polynomial is quintic.
• The multiplicative inverse $\frac{1}{a}$ have degree -1
• The square root has a degree as $\frac{1}{2}$
• The logarithm has a degree as 0, example log b.
• The exponential function’s degree is infinity.

In this section, learn how to find the degree of polynomial -

Using one variable:

Let us consider the polynomial, 8x³ + 7x⁴ + 6x² + 5x + 1.

The degree of the first term is 3.

The degree of the second term is 4

The degree of the third term is 2

The degree of the fourth term is 1 and

The degree of the last term is 0.

Here the greatest degree among all the degrees is 4. So the degree of the polynomial

8x³+7x⁴+6x²+5x+1 is 4.

Using two variables:

Let us consider the given polynomial is 5x²y⁴+2xy³+8y²+2y+x³+1

The degree of the first term is sum of the power of x and y. So the degree for the first term is 2+4 which is 6.

The degree of the second term is 1+ 3=4.

The degree of the third term is 2.

The degree of the fourth term is 1.

The degree of the fifth term is 3 and

The degree of the last term is 0.

Here the maximum degree is 4.
So 4 is the degree of the polynomial 5x²y⁴+2xy³+8y²+2y+x³+1