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
$f(x)=4 x^{4}-3 x^{3}-2 x^{2}+x-7, g(x)=x-1$
Solution:
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