The sum of the exponents in the first term is equal to 1.
The sum of the exponents in the second term is equal to 0.
The term with the highest sum of exponents determines the degree of the polynomial.
The degree of the polynomial is the sum of the exponents in that term.
The degree of your polynomial is equal to 1.
The fact that the constants had exponents attached to them doesn't count.
It's the exponents of the variables in each term of the polynomial that count.
A constant raised to any power is still a constant.
The rules for what is a polynomial are reasonably simple, but the determination of whether a polynomial fits those rules can get complicated.
It's best to simplify the polynomial as much as possible before deciding.
A polynomial that looks like it violates the rules before simplification may turn out to not violate the rules after simplification.
The rules are:
The exponents of the variables have to be zero or positive only.
The exponents of the variables have to be integer only.
The terms in the expression can be added or subtracted from each other only.
The variables within each term have to be multiplied by each other only.
Some examples:
sqrt(x) = x^(1/2) which is not allowed.
sqrt(x^2) = x which is allowed.
x/5 = (1/5)*x which is allowed.
5/x = 5*(1/x) = 5*x^(-1) which is not allowed.
x*y is allowed.
x/y is not allowed.
Dividing a variable by a constant is allowed.
Dividing a constant by a variable is not.
Dividing a variable by another variable is not.
Your expression didn't really violate any rules but they threw you a curve by showing the constants with exponents.
All you have to remember is that a constant is still a constant regardless of what power it is raised to.
It's the degree of the variable that counts, not the degree of the constant.
The degree of a constant is always equal to 0 after you have simplified the constant as much as possible.
Example;
Any variable name can be used to prove the point since any variable raised to the 0 power is equal to 1.
The degree of a variable without an exponent attached is equal to 1.
Example:
Examples of terms and the degree of the term:
= degree of 5 = degree of 5 because the sum of the exponents is equal to 0 + 5. = degree of 6 because the sum of the exponents is equal to 0 + 5 + 1. = degree of 9 because the sum of the exponents is equal to 0 + 3 + 4 + 2.
