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)

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11