Factor x^3 - 6x^2 + 11x - 6.

Factor x^3 - 6x^2 + 11x - 6.

• A. (x - 1)(x - 3)(x - 4)
• B. (x - 1)(x - 2)(x - 6)
• C. (x - 2)(x - 3)(x - 4)
• D. (x - 1)(x - 2)(x - 3)

Answer: (D)

Finding where the expression equals zero and writing the polynomial as a product of linear factors. If you plug in 1, you get 1 - 6 + 11 - 6 = 0, so x - 1 is a factor. Dividing the cubic by (x - 1) gives x^2 - 5x + 6. That quadratic factors nicely as (x - 2)(x - 3). Multiplying back together, (x - 1)(x - 2)(x - 3) expands to x^3 - 6x^2 + 11x - 6, which matches the original expression. So the factorization is (x - 1)(x - 2)(x - 3).

Finding where the expression equals zero and writing the polynomial as a product of linear factors. If you plug in 1, you get 1 - 6 + 11 - 6 = 0, so x - 1 is a factor. Dividing the cubic by (x - 1) gives x^2 - 5x + 6. That quadratic factors nicely as (x - 2)(x - 3). Multiplying back together, (x - 1)(x - 2)(x - 3) expands to x^3 - 6x^2 + 11x - 6, which matches the original expression. So the factorization is (x - 1)(x - 2)(x - 3).