After performing polynomial division of $x^3-3x^2+3x-1$ by $x-1$, what is the quotient?

Step-by-step solution

1. Use synthetic division with root $1$.
2. Set up the coefficients: 1 | -3 | 3 | -1.
3. Bring down the leading coefficient 1 to the bottom row.
4. Multiply 1 by 1 and add to the next coefficient: -3 + 1 = -2.
5. Multiply -2 by 1 and add to the next: 3 + (-2) = 1.
6. Multiply 1 by 1 and add to the last: -1 + 1 = 0 (remainder).
7. The bottom row gives the coefficients of the quotient: $1x^2-2x+1$.
8. Thus the quotient is $x^2-2x+1$.
9. The remainder is 0, confirming the division is exact.

Concept tested: Polynomial long division

Published 10 October 2026 · How this solution was prepared and checked