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

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Solution

verification
putting x=1 in f(x) we get

$f (1) = 1^{4} + 1 = 1 + 1 = 2 = r e m i n d e r$

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Question 13
By actual division, find the quotient and the remainder when the first polynomial $x^{4} + 1$ is divided by the polynomial (x - 1)

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

g (x) = x - 2

x^{4} + 1

x - 1

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

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