Question

Find the degree of each algebraic expression:
 $ 2{{y}^{2}}z+10yz $

Answer 1

Hint: We know that the degree of a polynomial of a given variable is the highest power which the variable has and we have to find the degree of the given polynomial i.e. $ 2{{y}^{2}}z+10yz $ as you can see that there are two variables in this algebraic expression y and z so the overall degree of this algebraic expression is the addition of the highest power of y and z.

Complete step-by-step answer:
The algebraic expression given in the above problem is:
 $ 2{{y}^{2}}z+10yz $
We are asked to evaluate the degree of this algebraic expression.
We know that, degree of any polynomial with a given variable is the highest power that a variable can have. Now, as you can see the algebraic expression $ 2{{y}^{2}}z+10yz $ has two variables y and z so we have to find the degree corresponding to each variable and then add the degrees to get the overall degree.
In the given algebraic expression:
  $ 2{{y}^{2}}z+10yz $
The degree corresponding to variable y is 2 because you can see that the highest power that y has is 2 and the degree corresponding to variable z is 1 so the overall degree is the summation of 2 and 1 which gives the result as 3.
Hence, the degree of the given algebraic expression is 3.

Note: The plausible mistake that could happen here is that you forget to consider the degree of z and have only considered the degree of y in the given algebraic expression.
 $ 2{{y}^{2}}z+10yz $
So, if you only consider the degree of y then the degree of the algebraic expression is 2 which is the wrong answer. Hence, make sure that you won’t make this mistake.
We can also derive one information from this problem which is like in this problem we have given two variables so we have separately found the degree of two variables and then add them so if we have given three different variables then we separately find the degree of three variables and then add them.Similarly, you can extend this approach to a higher number of variables too.