Given a polynomial
$$p(x) = a_0 +a_1+a_2x^2+\cdots + a_nx^n$$
it is possible to express \(p(x)\) in the algebraically equivalent
form
$$p(x) = a_0 + x\left(a_1+x\left(a_2+\cdots + x\left(a_{n-1} +xa_n
\right)\cdots\right)\right)$$
which is much more efficient for evaluation, as it requires only \(n\)
multiplications and \(n\) additions, and this is optimal. But this is
not implemented here because it's efficient. It is implemented because
it works if \(x\) is itself a (multivariate) polynomial, and that is
the second coolest thing ever. The coolest thing ever is the
Reduce() function.