InterviewSolution
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InterviewSolution
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Use factor theorem to verify that `x+a`is a factor of `x^n+a^n`for any odd positive integer. |
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Answer» `(-1)*(-1)=` `1*(-1)=(-1)` `(-1)*(-1)*(-1)=(-1)^3=(-1)` `(-1)^n=1` when n is even `(-1)^n=-1` when n is odd. `f(x)=x^n+a^n` `x=-a`and then Remainder=0 `f(-a)=(-a)^n+a^n` `=(-a)^n(a)^n+a^n` `=a^n[1-(-1)^n]=0` `1+(-1)^n=0` `(-1)^n=-1` It is possible only when n is odd. |
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