# How do you use the rational roots theorem to find all possible zeros of #f(x) = 3x^3 + 39x^2 + 39x + 27#?

##### 1 Answer

See explanation...

#### Explanation:

Before applying the rational roots theorem, note that all of the coefficients are divisible by

#f(x) = 3x^3+39x^2+39x+27 = 3(x^3+13x^2+13x+9)#

Then applying the rational roots theorem to the remaining cubic factor, we can deduce that any *rational* zeros of

That means that the only possible rational zeros are:

#+-1# ,#+-3# ,#+-9#

In addition note that all of the coefficients are positive, so there are no zeros for positive values of

#-1# ,#-3# ,#-9#

None of these is a zero, so

That is as much as we can learn from the rational roots theorem.

In fact