Final answer:
The factored form of 3x³ - 15x² + 18x is 3x(x - 2)(x - 3), which is accomplished by first factoring out the common term 3x and then factoring the quadratic expression.
Step-by-step explanation:
The question requires us to factor the expression 3x³ - 15x² + 18x. To find the correct factored form, we first look for any common factors in all three terms. We can see that all the terms have a common factor of 3x. Taking 3x out as a common factor, our expression becomes 3x(x² - 5x + 6).
The quadratic expression x² - 5x + 6 can be factored further. We need to find two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of x). These numbers are -2 and -3. Thus, factoring x² - 5x + 6 we get (x - 2)(x - 3).
Combining the factored parts, the full factored form of the expression is 3x(x - 2)(x - 3), which corresponds to option 3 from the given choices.