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

(N/A) To divide $p(x) = x^{3} - 3x^{2} + 5x - 3$ by $g(x) = x^{2} - 2$:
$1$. Divide the first term of the dividend $(x^{3})$ by the first term of the divisor $(x^{2})$ to get $x$. This is the first term of the quotient.
$2$. Multiply $x$ by $(x^{2} - 2)$ to get $x^{3} - 2x$. Subtract this from $p(x)$ to get $-3x^{2} + 7x - 3$.
$3$. Divide the first term of the new dividend $(-3x^{2})$ by the first term of the divisor $(x^{2})$ to get $-3$. This is the second term of the quotient.
$4$. Multiply $-3$ by $(x^{2} - 2)$ to get $-3x^{2} + 6$. Subtract this from the current remainder to get $7x - 9$.
Thus,the quotient is $x - 3$ and the remainder is $7x - 9$.