Final answer:
The greatest common factor of the terms in the polynomial 3x³ - 3x² - 18x is 3x(x - 3)(x + 2).
Step-by-step explanation:
The greatest common factor (GCF) of the terms in the polynomial 3x³ - 3x² - 18x can be found by factoring out the common factors of each term and then finding the greatest common factor of those factors.
Step 1: Factor out the common factor.
3x³ - 3x² - 18x = 3x(x² - x - 6)
Step 2: Factor the quadratic expression inside the parentheses.
x² - x - 6 = (x - 3)(x + 2)
Step 3: Identify the common factors.
The common factors are 3x and (x - 3)(x + 2)
Step 4: Find the greatest common factor.
Therefore, the greatest common factor of the terms in the polynomial is 3x(x - 3)(x + 2)