Give an example of polynomial $f (x), g (x), q (x)$ and $r (x)$ satisfying $f (x) = g (x) q (x) + r (x)$ where
i) $d e g r (x) = 0$
ii) $d e g q (x) = d e g r (x)$

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Solution

Degree of $x (x) = 0$
That means any constant remainder
$f (x)$ can be $= x^{.2} + 4 x + 3$
$g (x)$ can be $= x + 1$
$q (x)$ can be $= x + 3$
$x (x)$ can be = $0$

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