Question

By actual division, find the quotient and the remainder when (x⁴ + 1) is divided by (x – 1).
Verify that remainder = f(1).

Answer 1

Let f(x) = x⁴ + 1 and g(x) = x – 1.



Quotient = x³ + x² + x + 1

Remainder = 2

Verification:

Putting x = 1 in f(x), we get

f(1) = 1⁴ + 1 = 1 + 1 = 2 = Remainder, when f(x) = x⁴ + 1 is divided by g(x) = x – 1