Question

Find the remainder when x1999 is divided by x^2– 1

Answer 1

Step-by-step explanation

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