# What are all the possible rational zeros for #f(x)=x^3+4x^2+5x+2# and how do you find all zeros?

##### 1 Answer

#### Explanation:

#f(x) = x^3+4x^2+5x+2#

By the rational roots theorem, any *rational* zeros of

So the only possible *rational* zeros are:

#+-1, +-2#

Note also that *rational* zeros.

We find:

#f(-1) = -1+4-5+2 = 0#

So

#x^3+4x^2+5x+2 = (x+1)(x^2+3x+2)#

The only possible rational zeros of the remaining quadratic are also

#x^2+3x+2 = (x+1)(x+2)#

So all the zeros of