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anonymous

  • one year ago

what is the remainder of the division problem shown below (x^3+2x^2-6x-9)/(x+2)

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  1. amistre64
    • one year ago
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    would you agree that: \[\frac{p(x)}{x-a}=q(x)+\frac{r(x)}{x-a}\]

  2. amistre64
    • one year ago
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    for example \[\frac 54=1+\frac14\]

  3. anonymous
    • one year ago
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    yes

  4. amistre64
    • one year ago
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    then lets simplify it, by multiply both sides by x-a \[p(x)=(x-a)~q(x)+r(x)\] do we still agree?

  5. anonymous
    • one year ago
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    yes we do

  6. amistre64
    • one year ago
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    now, let x=a \[p(a)=\underbrace{(a-a)}_{\color{red}{=0}}~q(a)+r(a)\] \[p(a)=r(a)\]

  7. amistre64
    • one year ago
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    now, how can we apply this to your question

  8. amistre64
    • one year ago
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    (x^3+2x^2-6x-9) / (x+2) = q(x) + r(x)/(x+2) x^3+2x^2-6x-9 = (x+2) q(x) + r(x) when does x+2 = 0?

  9. anonymous
    • one year ago
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    ok thanks i got it from here

  10. amistre64
    • one year ago
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    good luck :)

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