In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):
f(x) = x4-3x2+4, g(x) = x-2
We have,
f(x) = x4-3x2+4 and g(x) = x-2
Therefore, by remainder theorem when f (x) is divided by g (x) = x – 2, the remainder is equal to f (2)
Now, f(x) = x4-3x2+4
f (2) = (2)4 – 3 (2)2 + 4
= 16 – 12 + 4
= 8
Hence, required remainder is 8.