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Factoring Polynomials

  1. Feb 5, 2010 #1
    Alright, I'll be honest. I was extremely tired and slept all through the lesson in Algebra today lol.
    And now I need help with factoring polynomials.

    Example problems that I need help on:
    7h3+448
    Perfect square factoring - y4-81
    Grouping - 3n3-10n2-48n+160

    You don't have to answer those problems (Though it would help =P), I just need a quick lesson or the formula for factoring these.
    Thanks =)
     
  2. jcsd
  3. Feb 5, 2010 #2
  4. Feb 5, 2010 #3

    HallsofIvy

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    The first thing I would do is try to factor out a 7: [itex]7(h^3- 64)[/itex] which is wonderful because it is now [itex]7(x^3- 4^3)[/itex].
    You need to know that [itex]a^2- b^3= (a- b)(a^2+ ab+ b^2)[/itex]

    Yes, those are perfect squares: [itex](y^2)^2- 9^2[/itex] and, of course, [itex]a^2- b^2= (a-b)(a+b)[/itex]. After you have used that you will still have a "difference of squares" in one factor and can use that again. There is no way to factor [math]a^2+ b^2[/math] with real coefficients.

    Well, 10 isn't divisible by 3 but 48 is so I would try [itex]3n^3- 48n= 3n(n^2- 16)[/itex]. Aha! Now it's easy to see that [itex]-10n^2+ 160= -10(n^2- 16)[/itex]

    [itex]3n^3- 10n- 48n+ 160= 3n(n^2- 16)- 10(n^2- 16)[/itex]
    That isn't the answer- you need to finish it.

     
  5. Feb 5, 2010 #4
    Thanks for the help, I knew it was something similar to this, just didn't know any formulas.
     
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