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Thread: Very urgent!

  1. #1
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    Unhappy Very urgent!

    I have 2 problems. I know that they're too easy but I don't know why my brain it's not working well.
    Divide the polynoms:
    1) X^6-1 : (x-1)
    2) x^4-4x^3+6x^2-4x-15 : (x-1)

    Any help will be appreciated!
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by blertta View Post
    I have 2 problems. I know that they're too easy but I don't know why my brain it's not working well.
    Divide the polynoms:
    1) X^6-1 : (x-1)
    $\displaystyle \frac{x^6-1}{x-1}$ : recognize the formula of a geometric series.

    2) x^4-4x^3+6x^2-4x-15 : (x-1)
    $\displaystyle =(x^4-x^3)-(3x^3-3x^2)+(3x^2-3x)-(x-1)-16$
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  3. #3
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    Do you know how to do long division of polynomials? For example, take $\displaystyle \frac{x^3 - 2x^2 + 3x - 2}{x - 1}$.

    How many times does $\displaystyle x - 1$ go into $\displaystyle x^3$?

    $\displaystyle x^2$ times. So, take $\displaystyle x^2(x - 1) = x^3 - x^2$ and subtract that from $\displaystyle x^3 - 2x^2 + 3x - 2$.
    You should get $\displaystyle -x^2 + 3x - 2$.

    How many times does $\displaystyle x - 1$ go into $\displaystyle -x^2$?

    $\displaystyle -x$ times. So, take $\displaystyle -x(x - 1) = -x^2 + x$ and subtract it from $\displaystyle -x^2 + 3x - 2$. You should get $\displaystyle 2x - 2$.

    How many times does $\displaystyle x - 1$ go into $\displaystyle 2x$?

    Twice. So take $\displaystyle 2(x - 1) = 2x - 2$ and subtract it from $\displaystyle 2x - 2$ and you are done.

    The final result of the division is $\displaystyle x^2 - x + 2$.
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