Q. Use remainder theorem to find remainder when polynomial x^6-1 is divided by x+1.

Soln:

Remainder Theorem:

Statement: “When polynomial f(x) is divided x-a then remainder is f(a).”

Here, f(x) = x^6-1

Comparing x + 1 with x – a

i.e. x – a = x + 1

or, -a = 1

a = -1

By remainder theorem, remainder is f(a) = f(-1)

R = f(-1) = (-1)^6 – 1

R = 1 -1 = 0

R = 0

Hence, remainder is 0 (Zero).