Question

Write the degree of the polynomial:
$$x^{5}y^{6}-7x^{3}y^{10}+20x^{5}y^{6}z^{5}$$

Answer 1

Hint: In this question it is given that we have to find the degree of the given polynomial $$x^{5}y^{6}-7x^{3}y^{10}+20x^{5}y^{6}z^{5}$$. So to find that, we have to find the degree of each individual 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 solution:
So here the expression is given,
$$x^{5}y^{6}-7x^{3}y^{10}+20x^{5}y^{6}z^{5}$$
Now we are going to find the degree of each term,
So the first term is $x^{5}y^{6}$, where the variables are x and y and the powers of x and y are 5 and 6 respectively.
Therefore, the degree of first term $x^{5}y^{6}$ = (power of x) + (power of y) = 5+6 =11
Similarly, for the second term $-7x^{3}y^{10}$ the variables are again x and y and their powers are 3 and 10 respectively.
Then the degree of second term $-7x^{3}y^{10}$ = 3+10 = 13.
Now for the third term $20x^{5}y^{6}z^{5}$, where the variables are x, y and z and their powers are 5, 6 and 5.
Therefore, the degree of third term $20x^{5}y^{6}z^{5}$ = 5+6+5 = 16
So from the above we observed that the degree of the third term is highest and it is 16.
Therefore, the degree of the given polynomial is 16.


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 coefficient 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 -).