Factor by grouping: x^3 - 3x^2 + 2x - 6.

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

Answer: (D)

Factoring by grouping looks for a common factor in pairs of terms so a common binomial can be pulled out. For x^3 - 3x^2 + 2x - 6, group the terms as (x^3 - 3x^2) and (2x - 6). Factor each group: x^2(x - 3) and 2(x - 3). Both groups share (x - 3), so factor it out: (x - 3)(x^2 + 2). The quadratic x^2 + 2 can’t be factored further over the real numbers, so this is the complete factorization.