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