Question

How do you state the degree of the polynomial $x{y^2} + 3xy - 7 + y$?

Answer 1

Hint: In this question, it is given that we have to find the degree of the given polynomial. So, to find that, we have to find the degree of each term. And then we need to select the highest degree among them. The highest degree of that particular individual term will be the degree of the polynomial.

Complete step-by-step answer:
So here the expression is given,
$ \Rightarrow x{y^2} + 3xy - 7 + y$
Now we are going to find the degree of each term,
So, the first term is $x{y^2}$, where the variables are x and y and the powers of x and y are 1 and 2 respectively.
$ \Rightarrow $ Degree of the first term $x{y^2}$ = (power of x) + (power of y)
Substitute the values,
$ \Rightarrow $ Degree of the first term $x{y^2} = 1 + 2$
Add the terms,
$ \Rightarrow $ Degree of the first term $x{y^2} = 3$
Similarly, for the second term $3xy$, where the variables are x and y and the powers of x and y are 1 and 1 respectively.
$ \Rightarrow $ Degree of second term $3xy$ = (power of x) + (power of y)
Substitute the values,
$ \Rightarrow $ Degree of the second term $3xy = 1 + 1$
Add the terms,
$ \Rightarrow $ Degree of the second term $3xy = 2$
Similarly, for the third term 7, the powers of x and y are 0 and 0 respectively.
$ \Rightarrow $ Degree of third term 7 = (power of x) + (power of y)
Substitute the values,
$ \Rightarrow $ Degree of the third term $7 = 0 + 0$
Add the terms,
$ \Rightarrow $ Degree of the third term $7 = 0$
Similarly, for the fourth term $y$, where the variable is y and the power of x and y are 0 and 1 respectively.
$ \Rightarrow $ Degree of the first term $y$ = (power of x) + (power of y)
Substitute the values,
$ \Rightarrow $ Degree of the first term $y = 0 + 1$
Add the terms,
$ \Rightarrow $ Degree of the first term $y = 1$
So, from the above, we observed that the degree of the first term is highest and it is 3.

Hence, the degree of the given polynomial is 3.

Note:
While finding the degree of a polynomial you need to know about the polynomial first, so a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables and every polynomial has a fixed degree.
The degree of a polynomial is the highest of the degrees of polynomial’s monomials (individual terms) with non-zero coefficients and the degree of the term is the sum of the exponents that appear in it. Also, the degree of each term does not depend on their sign(+ or -).