factor this
posted by John Levenstein at
7:23 PM
Monday, December 17, 2007
Contributors
Previous Posts
- A Great Bargain
- Me! Of all people!
- "The Bronx is Burning"
- "Mad Men"
- Recreational Mathematics
- accountability
- The Locker Puzzle
- Absentmindedness
- Kommune Kutz for Kidz
- The Golden Compass
Subscribe to
Posts [Atom]
30 Comments:
I'm pretty sure the answer is
((x^2) - 10.90833...) ((x^2) - 0.091673...)
but if that's truly the answer then I also believe that you don't really think it's a fantastic factoring problem and that you posted it to fuck with us.
Total time: 17 minutes.
That's correct within four decimal digits. The coefficients of the factors themselves are not rational.
Robert, don't factor with decimals. Seriously.
Why?
((x^2) - (10 + (90,833/100,000))) ((x^2) - (91,673/1,000,000))
Are you happier now, Bernie?
robert, a little less brain power, a bit more intuition.
John, you've been foiled again (pun intended).
Did you ever notice that when people say "no pun intended", what they really mean is "pun intended, and I'm even pointing out the existence of the pun just in case you didn't catch it"
(x - pi) (x + e)
That's what my intuition says, anyway.
i'm giving a big fucking hint. i have to because i just gave it to bernie. you have to add and subtract the same thing to make it a difference of squares. once you can put it in the form a^2 - b^2, you can reduce it to (a+b)(a-b). but you have to add and subtract something that puts it in that form.
i can't take you by the hand anymore than i already have. either you're nerds or you're not.
> but you have to add and subtract something that puts it in that form.
Pi?
That was a joke! Just a joke! And just because I haven't answered your hint yet doesn't mean I don't intend to!
I've got some of my nerdiest friends working on this too. We're all a bit baffled, but also intrigued because there are some oddities here.
Oh - by "some" I mean "one". But he's very nerdy!
John, you can add and subtract 25(x^2) to get
x^4 + 25(x^2) - 36(x^2) + 1
which "simplifies" to
((x^2 + 5x)(x^2 - 5x)) - ((6x + 1)(6x - 1))
but that's not a real satisfying answer, and isn't any simpler, actually. So I assume you have something else in mind?
Whatever you do, please don't post the answer to this great great puzzle yet!
(more serious than you might think).
i have something else in mind. i would never consider something "factored" that has a minus sign in the middle like that (i'll take a minus sign inside the parentheses, of course)
John, how arbitrary is the "11" in the "11x^2"? Are there other integers that would yield similar solutions? Would there be similar solutions for ALL integers? An infinite subset? A finite subset? Or only the number 11?
this is based on a problem in a math tournament i was in when we were in high school. but there is more than one version of the problem. they don't all involve the number 11. i don't have any reason to believe the high school math tournament question had the number 11. but for what i presented, it's crucial.
x^4-(11x^2)+1+9-9
leads to
(x^2-10)(x^2-1)-9
which probably leads further, but I need to go shovel the sidewalk.
the answer will be posted today. the key is adding and subtracting something that creates the difference of two squares.
Please don't post the answer yet!
One more day.
I give up.
x^4-11x^2+1
x^4-11x^2+9x^2+1-9x^2
x^4-2x^2+1-9x^2
(x^2-1)^2-(3x)^2
a^2-b^2=(a+b)(a-b)
so this equals...
(x^2+3x-1)(x^2-3x-1)
Did you solve the problem in the math tournament?
i did not solve the question in the tournament.
Perhaps you would have gotten it if you were on performance enhancing drugs
http://chronicle.com/daily/2007/12/1052n.htm
i think i would have gotten it if someone had told me i needed to add and subtract the same thing to make it the difference of squares. and then given me two days.
Paul has a point. Someone needs to poke around all competitive venues to check for performance-enhancing drugs.
You remembered the question from the tournament, which is remarkable in itself. I came across my high school yearbook recently ("sophomore" is spelled "sophmore" every single time) and learned that I was on the math team. I have no memories of this.
Post a Comment
<< Home