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

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sauravshakyaBest ResponseYou've already chosen the best response.1
Let f(x)=x^r +1 Now, use remainder theorem
 one year ago

frxBest ResponseYou've already chosen the best response.0
Don't know the remainder theorem :/
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
If a polynomial f(x) is divided by (xa) then (xa) is a factor of f(x) if f(a)=0.
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Oh sorry... it is Factor Theorem.... Now use this factor theorem.
 one year ago

frxBest ResponseYou've already chosen the best response.0
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?
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
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
 one year ago

frxBest ResponseYou've already chosen the best response.0
Oh, how stupid, I see that it's just a continuation of the factor theorm, thank you :)
 one year ago
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