Using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the by actual division
Question:
Using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the by actual division
$f(x)=x^{4}-3 x^{2}+4, g(x)=x-2$
Solution:
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