Final answer:
To factor the expression completely, use factoring by grouping or synthetic division to factor out the common factors and then apply difference of squares.
Step-by-step explanation:
To factor the expression completely: x³ - 3x² - 4x - 12, we can use factoring by grouping or synthetic division.
If we group the terms, we can factor out the greatest common factor from each pair of terms:
x²(x - 3) - 4(x - 3)
Now, we have a common factor of (x - 3), so we can factor it out:
(x - 3)(x² - 4)
The expression x² - 4 is difference of squares, so we can factor it further:
(x - 3)(x + 2)(x - 2)
Therefore, the correct factorization is option a. (x - 2)(x + 2)(x - 3).