Question

Remainder when x2009 is divided by (x2−1)
is

Answer 1

Answers:-

p(x)= x^1999

factors of x^2-1=(x+1)(x-1)

we know,

dividend=divisor*quotient+remainder

since p(x) is a polynomial of degree 1999 so it will leave a linear remainder in form of ax+b where a and b are constants.

x^1999=divisor*(x+1)(x-1)+ax+b

put x=1

so, 1=a+b                            ...(i)

put x=-1

so, -1=-a+b                     ...(ii)

solving equations

we get,

a=1 and b=0

so remainder=ax+b=1*x+0=x

so when x^1999 is divided by x^2-1 then it leaves remainder as x.

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Answer 2

hope so it will helpful to you