# How do you use the rational roots theorem to find all possible zeros of #f(x) = x^3 - 12x - 16#?

##### 1 Answer

#### Answer:

The zeros of this

#x=-2# with multiplicity#2#

#x=4#

#### Explanation:

By the rational roots theorem, any rational zeros of

That means that the only possible *rational* zeros are:

#+-1# ,#+-2# ,#+-4# ,#+-8# ,#+-16#

Also note that the signs of the coefficients of

So start trying the positive possibilities first:

#f(1) = 1-12-16 = -27#

#f(2) = 8-24-16 = -32#

#f(4) = 64-48-16 = 0#

So

#x^3-12x-16 = (x-4)(x^2+4x+4) = (x-4)(x+2)(x+2)#

So