Question

Write the degree of the following polynomial as below:
\[xyz-3\]

Answer 1

Hint: First of all we will have to know about the degree of polynomial. The degree of a polynomial is the greatest degree of a variable present in the polynomial expression. It indicates the highest exponential power in the polynomial. Let us consider if we have a polynomial \[{{x}^{a}}{{y}^{b}}{{z}^{c}}\] then its degree is equal to the sum \[\left( a+b+c \right)\].

Complete step-by-step answer:
We have been given to find the degree of the polynomial \[xyz-3\].
Now we know that the degree of a polynomial is the greatest degree of a variable present in the polynomial expression.
Let us suppose we have a polynomial \[{{x}^{a}}{{y}^{b}}{{z}^{c}}+t\] where a, b, c and t are constants. Then the degree of the polynomial is equal to the sum of degrees of the monomial terms present in the polynomial.
Hence, degree of polynomial = sum of degrees of \[\left( {{x}^{a}}{{y}^{b}}{{z}^{c}} \right)\] = \[\left( a+b+c \right)\].
We have the polynomial \[xyz-3\].
Degree of xyz \[={{x}^{1}}{{y}^{1}}{{z}^{1}}=1+1+1=3\]
Degree of (-3) = 0
Since we know that the degree of a constant term is zero.
Now we know that the degree of a polynomial is the highest degree of all its terms.
So degree of the polynomial = 3
Therefore, the degree of the given polynomial is equal to 3.

Note: Remember that degree of the polynomial is the greatest degree of a variable present in the polynomial. Also in this type of questions, we should check that the given expression is polynomial or not. Also, remember that the degree of a constant term is equal to zero.