Final answer:
To factor the expression 3x³ - 5x² - 24x + 16 into linear factors, use the given zero -4 and perform long division or synthetic division. The correct answer choice is A) (x + 4)(3x - 4)(x - 1).
Step-by-step explanation:
To factor the expression 3x³ - 5x² - 24x + 16 into linear factors, we can start by using the given zero, -4. This means that (x + 4) is one of the factors. To find the other factors, we can use long division or synthetic division. After dividing 3x³ - 5x² - 24x + 16 by (x + 4), we get 3x² - 17x + 4. This quadratic expression can be factored as (3x - 4)(x - 1). Therefore, the linear factors of the original expression are (x + 4)(3x - 4)(x - 1), which corresponds to answer choice A).