Question

Write the degree of the following polynomial $ - 8m{n^6} + 5{m^3}n$

Answer 1

Hint: According to the question we have to determine the degree of the given polynomial $ - 8m{n^6} + 5{m^3}n$ but first of all we have to understand about the degree.
So, the degree of a polynomial is the highest of the degree of the given polynomial with non-zero coefficient and the degree of a term is the sum of the exponent of the variables that appears in it, and thus is a non-negative integer.

Complete step-by-step answer:
Step 1: First of all we will find the variable term which has the maximum power so, now as we can see that as given in the expression/equation $ - 8m{n^6} + 5{m^3}n$ term $ - 8m{n^6}$ in which the variable n has the maximum degree which is 6.
Step 2: Now, we have to find the maximum coefficient of the given polynomial.
Hence, as we have obtained $ - 8m{n^6}$ in which the variable n has the maximum degree which is 6.
And in the term $5{m^3}n$ in which the variable n has degree which is 1 and m has a degree 3, so the total degree is 4.
For the term $ - 8m{n^6}$, m has a degree of 1 and n has a degree of 6.
So the degree of the polynomial will be the highest degree among the two variables.
By looking at the variables we can say that $ - 8m{n^6}$ has the highest degree
So the degree of the polynomial will be
$
   = 6 + 1 \\
   = 7
 $

Hence, we have obtained the maximum degree of the given polynomial $ - 8m{n^6} + 5{m^3}n$$ = 7$

Note: Polynomial: A polynomial is a mathematical expression/equation of one or more algebraic terms each of which consists of a constant multiplied by one more variable raised to a non-negative integral power.
A polynomial can have constants, variables and exponent, that can be combined using addition, subtraction, multiplication, and division but no division by a variable.
A number used to multiply a variable or a variable or number that is multiplied with another variable is known as the coefficient of that variable or number.