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

Here, $f(x)=4 x^{4}-3 x^{3}-2 x^{2}+x-7$

g(x) = x - 1

from, the remainder theorem when f(x) is divided by g(x) = x - (-1) the remainder will be equal to f(1)

Let, g(x) = 0

⟹ x - 1 = 0

⟹ x = 1

Substitute the value of x in f(x)

$f(1)=4(1)^{4}-3(1)^{3}-2(1)^{2}+1-7$

= 4 - 3 - 2 + 1 - 7

= 5 - 12

= -7

Therefore, the remainder is 7