How to Find the Degree of a Polynomial with More Than One Variables? (original) (raw)

Last Updated : 23 Jul, 2025

Answer: If a polynomial has multiple variables, the degree of the polynomial can be found by adding the powers of different variables in any terms present in the polynomial expression.

When dealing with polynomials in more than one variable, the degree of a term is the sum of the exponents of its variables. The degree of the polynomial is then determined by identifying the term with the highest total exponent.

**Step 1: Consider a Polynomial in Multiple Variables-
A polynomial in multiple variables looks like _P(_x, _y, _z, …) and consists of terms with various combinations of these variables.

**Step 2: Examine Each Term-
Each term in the polynomial is of the form _ax n, where _a is the coefficient and _n is the sum of the exponents of the variables in that term.

**Step 3: Add Exponents of Variables-
For each term, add the exponents of all the variables. For example, if you have a term 3__x_2__y_4__z_, the total exponent is 2+4+1=7.

**Step 4: Identify the Term with the Highest Exponent-
Look at all the terms in the polynomial and identify the term with the highest total exponent. The degree of the polynomial is then equal to this highest exponent.

**Step 5: Degree of the Polynomial-
The degree of the polynomial is the maximum sum of exponents found in any term. For example, if the term with the highest total exponent is 5__x_3__y_2, then the degree of the polynomial is 5.

To find the degree of a polynomial with more than one variable, add the exponents of the variables in each term and identify the term with the highest total exponent.

Similar Questions

**Problem 1: Find degree of 3x 2 y 3 z 4 .

**Solution:

Degree of 3x2y3z4 is = 2 + 3 + 4 = 9

**Problem 2: Find degree of x 2 y 3 **- x 2 y 2 + 2x.

**Solution:

Now, Degree of x2y3 is = 2 + 3 = 5
Degree of x2y2 is = 2 + 2 = 4
Degree of 2x = 1

So, Degree of highest term present in this polynomial is = 5.
Hence Degree of x2y3 - x2y2 + 2x is 5

**Problem 3: Find degree of 4x 2 y - 5x 4 y 2 + 19x 2 y 2 .

**Solution:

Now, Degree of 4x2y is = 2 + 1 = 3
Degree of 5x4y2 is = 4 + 2 = 6
Degree of 19x2y2 = 2 + 2 = 4

So, Degree of highest term present in this polynomial is = 6.
Hence Degree of 4x2y - 5x4y2 + 19x2y2 is 6

**Problem 4: Find degree of 2xy + 4yz.

**Solution:

Now, Degree of 2xy is = 1 + 1 = 2
Degree of 4yz is = 1 + 1 = 2

So, Degree of highest term present in this polynomial is = 2.
Hence Degree of 2xy + 4yz is 2