Determine the quotient when the polynomial is divided by the binomial: \[ \left(x^{3}+4 x^{2}-8 x+3\right) \div(x-1) \]

Step 1 ：\(\frac{x^3 + 4x^2 - 8x + 3}{x - 1}\)

Step 2 ：Divide the first term of the dividend \(x^3\) by the first term of the divisor \(x\) to get \(x^2\)

Step 3 ：Multiply the divisor \(x - 1\) by \(x^2\) and subtract this from the dividend to get \(5x^2 - 8x\)

Step 4 ：Divide the first term of the new dividend \(5x^2\) by the first term of the divisor \(x\) to get \(5x\)

Step 5 ：Multiply the divisor \(x - 1\) by \(5x\) and subtract this from the new dividend to get \(-3x + 3\)

Step 6 ：Divide the first term of the new dividend \(-3x\) by the first term of the divisor \(x\) to get \(-3\)

Step 7 ：Multiply the divisor \(x - 1\) by \(-3\) and subtract this from the new dividend to get 0

Step 8 ：\(\boxed{x^2 + 5x - 3}\) is the quotient of the polynomial and the binomial