# How do you determine the degree, terms and coefficients or the following polynomial 3x^7?

The degree is the highest power of $x$, which is 7. There's only one term for this polynomial, the polynomial $3 {x}^{7}$ itself. And there's only one coefficient, $3$ (in addition, if you prefer, you can also say all the coefficients of the lower powers of $x$ are zero).
For a general polynomial $f \left(x\right) = {a}_{n} {x}^{n} + {a}_{n - 1} {x}^{n - 1} + {a}_{n - 2} {x}^{n - 2} + \setminus \cdots + {a}_{2} {x}^{2} + {a}_{1} x + {a}_{0}$, where ${a}_{n} \ne 0$, the degree is $n$, the terms are the terms you see for those $a$'s that are nonzero, and the coefficients are ${a}_{n} , {a}_{n - 1} , {a}_{n - 2} , \setminus \ldots , {a}_{2} , {a}_{1} , {a}_{0}$. Whether you decide to include those $a$'s that are zero in your list of coefficients is, in a sense, dependent on what you are doing with the polynomial.
For example, if you are graphing it, then you don't need to worry about the $a$'s that are zero. On the other hand, if you are using synthetic division to confirm a root of the polynomial (or to divide it by $x - c$), then the $a$'s that are zero are important to include in your calculation.