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How to factor this monster into two quadratics?

  1. Mar 23, 2008 #1
    1. The problem statement, all variables and given/known data

    How to factor this monster? I am rather clueless
    [tex]144t^{4}-288t^{3}+864t^{2}-720t+900[/tex]

    2. Relevant equations

    Hint is given that you can get two quadratic polynomials out of it..

    3. The attempt at a solution

    I can always cheat by using Maple to factor but I don't want do it! I want learn how to do it.

    Thanks for any help!
     
  2. jcsd
  3. Mar 23, 2008 #2

    tiny-tim

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    Hi motornoob! :smile:

    Well, for a start, you can divide by 36 to get:

    [tex]4t^{4}\,-\,8t^{3}\,+\,24t^{2}\,-\,20t\,+\,25[/tex]​

    hmm … now to think … :frown:
     
  4. Mar 23, 2008 #3
    Yeah I divided by 144 to get something smaller but the last number is like 6.25.. I said is no big deal.. but still, I can't factor this.
     
  5. Mar 23, 2008 #4

    tiny-tim

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    motornoob, there's no point in making fractions - the object is to simplify it!

    Stick with mine:
    [tex]4t^{4}\,-\,8t^{3}\,+\,24t^{2}\,-\,20t\,+\,25[/tex]​

    I think the best way to do this is just to write it as

    [tex](at^{2}\,+\,bt\,+\,c)(dt^{2}\,+\,et\,+\,f)\,,[/tex] ​

    and just multiply it out, giving you five equations to solve.

    (I've done it - you can more-or-less guess the right answer once you've done that.)

    Have a go! :smile:
     
  6. Mar 23, 2008 #5
    Five equations to solve huh. I sure hope they don't give us something like this on an exam, considering this part of an integration problem. Thanks so much for the help.
     
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