Here's the question you clicked on:
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Show that if r is a positive odd integer then the polynomial \[x ^{r}+1\] is dividable by \[x+1\]
Let f(x)=x^r +1 Now, use remainder theorem
Don't know the remainder theorem :/
If a polynomial f(x) is divided by (x-a) then (x-a) is a factor of f(x) if f(a)=0.
Oh sorry... it is Factor Theorem.... Now use this factor theorem.
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?
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
Oh, how stupid, I see that it's just a continuation of the factor theorm, thank you :)