When dividing x^3 - 6x^2 + 11x - 6 by (x - 1), what is the remainder?

• A. 6
• B. 0
• C. 1
• D. -1

Answer: (B)

When you divide by x minus 1, use the Remainder Theorem: the remainder is the value of the polynomial at x = 1. For P(x) = x^3 - 6x^2 + 11x - 6, compute P(1) = 1 - 6 + 11 - 6 = 0. So the remainder is 0, meaning x - 1 is a factor of the polynomial. It also factors as (x - 1)(x - 2)(x - 3).