Divide $x^{3}-3x^{2}+5x-3$ by $x^{2}-2$.

(N/A) Given dividend $p(x) = x^{3}-3x^{2}+5x-3$ and divisor $s(x) = x^{2}-2$.
Step $1$: Divide the first term of the dividend $(x^{3})$ by the first term of the divisor $(x^{2})$ to get $x$. Multiply $x$ by $(x^{2}-2)$ to get $x^{3}-2x$. Subtract this from the dividend: $(x^{3}-3x^{2}+5x-3) - (x^{3}-2x) = -3x^{2}+7x-3$.
Step $2$: Divide the first term of the new polynomial $(-3x^{2})$ by the first term of the divisor $(x^{2})$ to get $-3$. Multiply $-3$ by $(x^{2}-2)$ to get $-3x^{2}+6$. Subtract this from the current polynomial: $(-3x^{2}+7x-3) - (-3x^{2}+6) = 7x-9$.
Thus,the quotient is $q(x) = x-3$ and the remainder is $r(x) = 7x-9$.