Using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the by actual division

Here, $f(x)=x^{4}-3 x^{2}+4$

g(x) = x - 2

from, the remainder theorem when f(x) is divided by g(x) = x - 2 the remainder will be equal to f(2)

Let, g(x) = 0

⟹ x - 2 = 0

⟹ x = 2

Substitute the value of x in f(x)

$f(2)=2^{4}-3(2)^{2}+4$

= 16 - (3* 4) + 4

= 16 - 12 + 4

= 20 - 12

= 8

Therefore, the remainder is 8