Find the remainder when $f (x) = x^{4} - 3 x^{2} + 4$ is divided by $g (x) = x - 2$ and verify the result by actual division

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Solution

Given : $f (x) = x^{4} - 3 x^{2} + 4$
$f (2) = (2)^{4} - 3 (2)^{2} + 4$
$= 16 - 12 + 4 = 8$
This can also be verified by the actual divison (attached in the figure)

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Similar questions

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division.

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

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division.

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

By actual division, find the quotient and the remainder when $(x^{4} + 1)$ is divided by (x - 1).
Verify that remainder = f(1).

p (x)

g (x)

p (x) = x^{4} - 3 x^{2} - 4; g (x) = x + 2