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

Last updated date: 24th Jul 2024
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Hint: To solve such questions always remember that the degree of any polynomial can be defined as the biggest degree associated with any term of the polynomial. Start by finding the degree of each of its terms separately and thus find the highest degree.

Given the polynomial $x{y^2} + 3xy - 7 + y$ .
It is asked to find the degree of the given polynomial.
So in the given polynomial $x{y^2} + 3xy - 7 + y$ consider the first term, that is,
$x{y^2}$
So here the degree can be found as follows:
$x{y^2} = {x^1}{y^2}$
Adding the exponents we get the degree of the term, that is,
$1 + 2 = 3$
So the degree of the first term $x{y^2}$ is $3$ .
Similarly consider the second term, that is,
$3\;xy$
So here the degree can be found as follows:
$3xy = 3{x^1}{y^1}$
Adding the exponents we get the degree of the term, that is,
$1 + 1 = 2$
So the degree of the second term $3\;xy$ is $2$ .
Next, consider the third term, that is,
$- 7$
This term does not have any degree.
Finally consider the fourth term, that is,
$y$
So here the degree can be found as follows:
$y = {y^1}$
So here the degree of the term $y$ will be $1$ .
Since we know that the degree of any polynomial is the biggest degree associated with any term of the polynomial, it can be seen that the degree of the given polynomial $x{y^2} + 3xy - 7 + y$ is $3$ .

Note: The mistake which can be made while solving this type of question is while adding the exponents. Always start by determining the exponents of each variable in the terms in the polynomial and then adding those exponents to get the degree of each term.