What is remainder when x^101 is divided by x^2 -1
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The condition of the remainder is ax+b.
The remainder will be linear or below because the dividend is 2nd degree.
Now, we have
We can rewrite R as ax+b.
Again, we have
As we don't know (x²-1)Q(x) we should make it zero.
x=1 and x=-1 make it zero.
1. Substitute 1
We have an equation 1=a+b here.
2. Substitute -1
We have an equation -1=-a+b here.
Linear Equation
As the value of a is 1 and b is 0, we can find the remainder.
So, R=ax+b=1x+0=x. Therefore, the remainder is x.
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