Math, asked by vampirevenem2040, 8 months ago

What is remainder when x^101 is divided by x^2 -1

Answers

Answered by TakenName
1

The condition of the remainder is ax+b.

The remainder will be linear or below because the dividend is 2nd degree.

Now, we have x^{101}=(x^2-1)Q(x)+R

We can rewrite R as ax+b.

Again, we have x^{101}=(x^2-1)Q(x)+ax+b

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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