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Polynomials stuff

  1. Sep 19, 2010 #1
    i'm pretty new to polynomials and I have qns, which I do not know how to solve.

    x5 + ax3 + bx2 - 3 = (x2 - 1)Q(x)- x - 2

    Q(x) is a polynomial. Solve a and b.

    I know the degree of Q(x) is 3, so I subst Q(x) into x3, but I got stuck.

    Help. Thanks in advance.
     
  2. jcsd
  3. Sep 19, 2010 #2

    Mentallic

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    You don't need to know what Q(x) is. The zeroes of [tex]x^2-1[/tex] are [tex]x=\pm 1[/tex] so if you substitute x=1 into the entire equality, that Q(x) part cancels since anything times zero is zero (your 'anything' is the Q(x)) and then you'll get an equation in a and b. Then substitute the other value of x to get another equation in a and b. Solve simultaneously and you're done! :smile:
     
  4. Sep 19, 2010 #3
    Thank you very much.

    How about this:

    4x3 + 5x - 2 = (x+2)(x-1)P(x) + ax + b

    Find a and b. Last qns, I seriously can't solve!
     
  5. Sep 19, 2010 #4

    Mentallic

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    If you thought a bit more about what I posted you should have picked up on what to do. What values of x can you choose so that you eliminate the P(x)?
     
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