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# Give examples of polynomials $p(x), g(x), q(x)$ and $r(x)$, which satisfy the division algorithm and deg $q(x) =$ deg $r(x)$

Given:

deg $q(x) =$ deg $r(x)$

To do:

We have to give examples of polynomials $p(x), g(x), q(x)$ and $r(x)$, which satisfy the division algorithm and deg $q(x) =$ deg $r(x)$

Solution:

$p(x), g(x), q(x), r(x)$

deg $q(x) =$ deg $r(x)$

This is possible when

deg of both $q(x)$ and $r(x)$ are less than $p(x)$ and $g(x)$.

$p(x) = x^3+ x^2 + x + 1$

$g(x) = x^2 - 1$

$q(x) = x + 1$

$r(x) = x + 2$

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