# How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=x^3-2x^2-8x#?

##### 1 Answer

The zeros of

#### Explanation:

Given:

#f(x) = x^3-2x^2-8x#

Note that the signs of the coefficients of

The signs of the coefficients of

In order to usefully apply the rational zeros theorem we need a non-zero constant term, but

#x^3-2x^2-8x = x(x^2-2x-8)#

Now applying the rational zeros theorem to

That means that its only possible rational zeros are:

#+-1, +-2, +-4, +-8#

Trying these, we find:

#(color(blue)(-2))^2-2(color(blue)(-2))-8 = 4+4-8 = 0#

#(color(blue)(4))^2-2(color(blue)(4))-8 = 16-8-8 = 0#

So the zeros of