Can you help me with this Pre-Calculus Problem?

Question

How do I find the number of real zeros for the function f (x)= x^3-2x^2-8x?

Answer 1

Factor it:  x^3-2x^2-8x? = x(x² -2x - 8) = 0

x(x-4)(x+2) = 0

 

This was not too hard and the rest is very easy.

Answer 2

Set f(x) equal to zero.

 

x³ - 2x² - 8x = 0

 

 

Factor the left side of equation.

 

x(x² - 2x - 8) = 0

 

x(x - 4)(x + 2) = 0

 

 

Set the factors equal to zero and solve for x.