given that - 4 is a zero of the function f (x) = x3+3x2-16x-48f (x) = x3+3x2-16x48, find the other zeros and write f (x) f (x) in factored form

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)