Find the remainder when x^2007 is divisible by (x^2-1)

Answers (1)

Here the remainder is assumed to be a linear since the divisor is a quadratic equation.
Therefore the remainder is in the form of=ax+b
So,x^2007=Quotient*(x^2-1)+(ax+b)
By hit and trail method,
Putting the value of x as 1,we see 1=0+(a+b) and
Putting the value of x as -1,we see -1^2007=-1=0+(-a+b)
Thus By simultaneously solving the above equations we get the value of b as 0 and the value of a as 1
	herefore Remainder=x+0=x

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