Answer:
f(x) = (x + 4)(x - 4)(x + 3)
The other zeros of the function are at 4 and -3.
Step-by-step explanation:
Given function is f(x) = x³ + 3x² - 16x - 48.
Now, given that - 4 is a zero of the given function.
So, the function has a factor equals to (x + 4).
Now, f(x) = x³ + 3x² - 16x - 48
⇒ f(x) = x³ + 4x² - x² - 4x - 12x - 48
⇒ f(x) = x²(x + 4) - x(x + 4) - 12(x + 4)
⇒ f(x) = (x + 4)(x² - x - 12)
⇒ f(x) = (x + 4)(x - 4)(x + 3)
Therefore, the other zeros of the function are at 4 and -3. (Answer)
