Jan 05, 2019
RAY: There are a lot of our little children that listen to Car Talk that are studying Algebra and I thought I would ask them to simplify the following polynomial.
X plus A in parentheses times X minus B in parentheses times X plus C in parentheses times X minus D in parenteses and so on and so on until times X minus Z.
So, (x+a) x (x-b) x (x+c) x (x-d) ... (x-z).
I want the product of all those terms.
RAY: And...the answer is zero!
If you go back two terms, the last letters of the alphabet are z, y, and x in reversed order. So before x-z would be x+y and the term before that would be x-x.
And of course, x-x is zero.