Question

How do you find the degree of a polynomial in two variables?

Answer 1

Hint: In the given question, we are asked as in how do we find the degree of a polynomial in two variables. We know that the degree of a polynomial is the maximum degree of the monomial (in two variables) within the given polynomial. So, the term in the polynomial having the maximum powers raised to the variables in the polynomial with a non-zero coefficient can be said to be the degree of a polynomial in two variables.

Complete step-by-step solution:
According to the given question, we are asked as in how do we find the degree of a polynomial in two variables.
Polynomial in two variables refers to a polynomial expression having two variables, say, \[x\] and \[y\].
Degree of a polynomial is the maximum degree of the monomial (in two variables) within the given polynomial.
Monomial refers to the single term in a polynomial expression. Examples of monomials in two variables –
1) \[x{{y}^{2}}\]: This has a degree of 3
2) \[{{x}^{2}}y\]: This has a degree of 3
3) \[{{y}^{4}}={{x}^{0}}{{y}^{4}}\]: This has a degree of 4
So, in a polynomial expression, the monomials are checked in order to find the degree of the polynomial expression. We just have to add the powers of the variables involved in the term or the monomial of a polynomial expression.
So, if we have a polynomial expression as,
\[2x{{y}^{3}}+3{{x}^{2}}y+xy\]
Then the monomials we have is,
1) \[2x{{y}^{3}}\]: This has a degree of 4
2) \[3{{x}^{2}}y\]: This has a degree of 3
3) \[xy\]: This has a degree of 2
So, we can see that the monomial \[2x{{y}^{3}}\] has the maximum degree.
Therefore, the degree of the polynomial \[2x{{y}^{3}}+3{{x}^{2}}y+xy\] is 4.

Note: We find the degree of a polynomial by adding up the powers of the variables in a monomial. Do not get confused with the above statement and add up the powers of the all the monomials present in the polynomial expression, because then it will be wrong. This should be clearly understood before computing the value of degree of the polynomial.