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
$f(x)=2 x^{4}-6 x^{3}+2 x^{2}-x+2, g(x)=x+2$
Solution:
Here, $f(x)=2 x^{4}-6 x^{3}+2 x^{2}-x+2$
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)
$f(-2)=2(-2)^{4}-6(-2)^{3}+2(-2)^{2}-(-2)+2$
= (2 * 16) - (6 * (-8)) + (2 * 4) + 2 + 2
= 32 + 48 + 8 + 2 + 2
= 92
Therefore, the remainder is 92