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frx

  • 2 years ago

Show that if r is a positive odd integer then the polynomial \[x ^{r}+1\] is dividable by \[x+1\]

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  1. sauravshakya
    • 2 years ago
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    Let f(x)=x^r +1 Now, use remainder theorem

  2. sauravshakya
    • 2 years ago
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    Can u?

  3. frx
    • 2 years ago
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    Don't know the remainder theorem :/

  4. sauravshakya
    • 2 years ago
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    If a polynomial f(x) is divided by (x-a) then (x-a) is a factor of f(x) if f(a)=0.

  5. sauravshakya
    • 2 years ago
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    Oh sorry... it is Factor Theorem.... Now use this factor theorem.

  6. frx
    • 2 years ago
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    I do get the factor theorem, so that proves a part of it. I do have the answer though and it says that this it only valid if and only if (-1)^r+1=0, what's the meaning of that?

  7. sauravshakya
    • 2 years ago
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    f(x)=x^r +1 Now, when f(x) id divided by (x+1) then, Remainder = f(-1)=(-1)^r+1 Since r is odd (-1)^r=-1 So, Remainder =f(-1)=-1+1=0 Thus,x^r +1 is divisible by x+1

  8. frx
    • 2 years ago
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    Oh, how stupid, I see that it's just a continuation of the factor theorm, thank you :)

  9. sauravshakya
    • 2 years ago
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    Welcome

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