Using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the by actual division :
f(x) = x4 – 3x2 + 4, g(x) = x – 2
Put g(x) = 0
⇒ x – 2 = 0 or x = 2
Remainder = f(2)
Now,
f(2) = (2)4 – 3(2)2 + 4
= 16 – 12 + 4
= 8
Actual Division:
