x^11 + 1 divided by x + 1. What will be the remainder? How to do it?

Thanks,

Ron

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- Feb 11th 2011, 04:25 PMrn5aExponents
x^11 + 1 divided by x + 1. What will be the remainder? How to do it?

Thanks,

Ron - Feb 11th 2011, 04:34 PMpickslides
If you use long division you should get $\displaystyle \displaystyle \frac{x^{11}+1}{x+1} = x^{10}-x^9+x^8-\dots +1$

- Feb 11th 2011, 04:35 PMrtblue
When you divide any degree polynomial and want to find the remainder, use the remainder theorm.

Set what you are dividing by to 0.

x+1=0 x=-1

Substitute -1 into x^11+1, and what you get is the remainder.