what is the quotient of $(x^{3}-3x^{2}+5x - 3)div(x - 1)$?\n$x^{2}-2x - 3$\n$x^{2}+2x + 7$\n$x^{2}-3x +…

Explanation:

Step1: Use polynomial long - division

We divide $x^{3}-3x^{2}+5x - 3$ by $x - 1$. First, divide the leading term of the dividend $x^{3}$ by the leading term of the divisor $x$. The result is $x^{2}$. Multiply $x - 1$ by $x^{2}$ to get $x^{3}-x^{2}$. Subtract this from the dividend: $(x^{3}-3x^{2}+5x - 3)-(x^{3}-x^{2})=-2x^{2}+5x - 3$.

Step2: Repeat the process

Divide the leading term of the new dividend $-2x^{2}$ by the leading term of the divisor $x$ to get $-2x$. Multiply $x - 1$ by $-2x$ to get $-2x^{2}+2x$. Subtract this from the new dividend: $(-2x^{2}+5x - 3)-(-2x^{2}+2x)=3x - 3$.

Step3: Final division

Divide the leading term of the new dividend $3x$ by the leading term of the divisor $x$ to get $3$. Multiply $x - 1$ by $3$ to get $3x - 3$. Subtract this from the new dividend: $(3x - 3)-(3x - 3)=0$.

Answer:

D. $x^{2}-2x + 3$