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

Here, $f(x)=x^{3}+4 x^{2}-3 x+10$

g(x) = x + 4

from, the remainder theorem when f(x) is divided by g(x) = x - (- 4)  the remainder will be equal to f(- 4)

Let, g(x) = 0

⟹ x + 4 = 0

⟹ x = - 4

Substitute the value of x in f(x)

$f(-4)=(-4)^{3}+4(-4)^{2}-3(-4)+10$

= - 64 + (4*16) + 12 + 10

= - 64 + 64 + 12 + 10

= 12 + 10

= 22

Therefore, the remainder is 22