Polynomials of Degree-n

In general, a polynomial in one variable and of degree n will have the following form:

\[p\left( x \right):{a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + ... + {a_1}x + {a_0},\,\,\,{a_n} \ne 0\]

We see that the maximum number of terms in a polynomial of degree n can be 1 more than n.

As shown above, the coefficients in a polynomial of degree n are generally represented as:

\[{a_n},{a_{n - 1}},...,{a_1},{a_0}\]

Also, we must have \({a_n} \ne {\rm{0}}\) otherwise the polynomial will not be of degree n.