A polynomial with a single variable is more or less what you would mean by "use base-infinity digits" in the first place. Roughly, in base 10, the number repre

A polynomial with a single variable is more or less what you would mean by "use base-infinity digits" in the first place. Roughly, in base 10, the number represented by the sequence of digits d_0, d_1, ..., d_n is d_0 + d_1 * 10 + d_2 * 10^2 + ... + d_n * 10^n. In "base infinity", the "number" represented by the sequence of digits d_0, d_1, ..., d_n is the polynomial d_0 + d_1 * x + d_2 * x^2 + ... + d_n * x^n. Multiplying these "numbers" (polynomials) is like decimal multiplication, except the digits can be arbitrarily high and you do no carrying at all.