How to Find the Degree of a Polynomial with More Than One Variables?

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 axⁿ, 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 3x²y⁴z, 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 5x³y², 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 3x²y³z⁴.

Solution:

Degree of 3x²y³z⁴ is = 2 + 3 + 4 = 9

Problem 2: Find degree of x²y³ - x²y² + 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 4x²y - 5x⁴y² + 19x²y².

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