Question

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

Answer 1

The degree is the highest power of `x`, which is 7. There's only one term for this polynomial, the polynomial `3x^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).

Explanation:

For a general polynomial `f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\cdots+a_{2}x^2+a_{1}x+a_{0}`, where `a_{n}!=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},\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.