Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

This is an MCQ we were posed in school recently (I hope you don't mind elementary stuff):

What is $(x-a)(x-b)(x-c)...(x-z)$ ? Options:





share|cite|improve this question
Are you sure it didn't go up to $x-z$? – mixedmath Sep 27 '12 at 2:56
@mixedmath Surely it did, or else none of the choices is correct (not that I particularly like the "solution" in that case). – Austin Mohr Sep 27 '12 at 2:58
Oh yes, it did. I'm so sorry. But the last option was still $x^n - (abc...z)$ AFAIK. I lost the test paper :( – Soham Chowdhury Sep 27 '12 at 2:59
How does it matter if it's $n$ or $z$? – Soham Chowdhury Sep 27 '12 at 3:01
@SohamChowdhury The fact that $n$ or $z$ actually makes a difference is something you should think about. – Erick Wong Sep 27 '12 at 3:07
up vote 7 down vote accepted

There is a very basic trick to this problem. It all comes down to a single term (if that's the proper word for it...).

The only real hint I can give is $x$ is a letter between $a$ and $z$...

share|cite|improve this answer
+1, Very cool! Also, Thank you @DonAntonio for pointing where I went wrong. – NoChance Sep 27 '12 at 4:11
Ah, I see... $(x-a)(x-b)..(x-x)..(x-z)$ where $(x-x)$ is 0. Nice! – Soham Chowdhury Sep 27 '12 at 4:22

Hint $\ $ What is $\rm\ (24-1)(24-2)(24-3)\cdots (24-26)\ $ ?

And what is $\rm\,(x_{24}\!-x_1)(x_{24}\!-x_2)(x_{24}\!-x_3)\cdots (x_{24}\!-x_{26})\ $ ?

share|cite|improve this answer
@Thanks for the hint. Very good point. – NoChance Sep 27 '12 at 4:08

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.