Divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder, in each of the following:
$p(x) =x^4 - 3x^2 + 4x + 5, g(x) = x^2 + 1 -x$

Given:

$p(x) =x^4 - 3x^2 + 4x + 5, g(x) = x^2 + 1 -x$

To do:

We have to divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder.

Solution:

$p(x) = x^4 - 3x^2 + 4x + 5$

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

Therefore, the quotient is $x^2+x-3$ and the remainder is $8$.