Polynomials are Numbers!

Published by Arun Isaac on

Tags: math

Polynomials are numbers of an unknown base x…

Everyone knows what numbers are. That's pretty much one among the earliest things we learn at school - even more vital to survival than written language. And then, we go on to learn how to do crazy stuff with numbers we never thought was possible otherwise. Well, that is talking about the beauty of mathematics… Some other day, maybe…

What I really wanted to say was how numbers and polynomials are connected. You see, the decimal number 49153 may be expanded by place value as

\[ 49153 = (4 \times 10^4) + (9 \times 10^3) + (1 \times 10^2) + (5 \times 10) + 3 \]

And, the binary number 110101 may be expanded by place value as

\[ 110101 = (1 \times 2^5) + (1 \times 2^4) + (0 \times 2^3) + (1 \times 2^2) + (0 \times 2) + 1 \]

And, in a similar fashion, a number of any other base may be expanded with its place value. Now, what few people really realize is that the polynomial is the generalization of a number! A polynomial is a number with an unknown base x.

\[ f(x) = 3x^3 + x^2 + 2x + 1 \]

In the above polynomial, 3, 1, 2 and 1 are the digits of this unknown number!

Ok… That's fine… You ask me what the point of all this is? Maybe I'll tell you sometime soon…