Answer:
x = 2; x = -1 ; x = -4
Explanation:
The zeroes of the function are the values of x where f(x) is zero. We can find these values by setting the function to zero and solving for those values of x.
Let x³ + 3x² - 6x - 8 = 0
Since the function cubic and has a term without x we first have to find a factor through trial and error to make factorization easy.
Since when x = 2; f(x) = (2³) + 3(2)² - 6(2) - 8 = 0
then ⇒ x - 2 = 0 is a factor of f(x) & x = 2 is a zero of the function
Now we can use the long division to factor f(x)
[see picture below for this step]
Now, since f(x) = (x - 2) (x² + 5x + 4)
then (x - 2) (x² + 5x + 4) = 0
⇒ x² + 5x + 4 = 0 [a] or x -2 = 0
Now let's factor [a]
x² + 5x + 4 = 0
x² + 4x + x + 4 = 0
(x + 1) (x + 4) = 0
⇒ x = 2 x = -1 ; x = -4 are the zeroes of the function