Explain remainder theorem with an example.

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Solution

Remainder Theorem : If p(x) is any polynomial of degree greater than or equal to 1 and p(x)
is divided by the linear polynomial x - a, then the remainder is p(a).
Example : $2 x^{2} - 5 x - 1$ divided by x-3
$f (x)$ is $2 x^{2} - 5 x - 1$
g(x) is x-3

After dividing we get the answer 2x+1, but there is a remainder of 2.
q(x) is 2x+1
r(x) is 2
In the style f(x) = g(x) . q(x) + r(x) we can write:
$2 x^{2} - 5 x - 1 = (x - 3) (2 x + 1) + 2$

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