Divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder in each of the following:
$p(x) = x^{4} - 5x + 6, \quad g(x) = 2 - x^{2}$

(N/A) To divide $p(x) = x^{4} - 5x + 6$ by $g(x) = -x^{2} + 2$,we arrange the terms in descending order of their degrees:
$p(x) = x^{4} + 0x^{3} + 0x^{2} - 5x + 6$
$g(x) = -x^{2} + 2$
Performing long division:
$1$. Divide the first term of $p(x)$ by the first term of $g(x)$: $x^{4} / (-x^{2}) = -x^{2}$. This is the first term of the quotient.
$2$. Multiply $-x^{2}$ by $(-x^{2} + 2)$ to get $x^{4} - 2x^{2}$. Subtract this from $p(x)$ to get $2x^{2} - 5x + 6$.
$3$. Divide the first term of the new polynomial $(2x^{2})$ by the first term of $g(x)$ $(-x^{2})$: $2x^{2} / (-x^{2}) = -2$. This is the second term of the quotient.
$4$. Multiply $-2$ by $(-x^{2} + 2)$ to get $2x^{2} - 4$. Subtract this from $2x^{2} - 5x + 6$ to get $-5x + 10$.
Thus,the quotient is $-x^{2} - 2$ and the remainder is $-5x + 10$.