# How do you find all the zeros of #F(x)=x^3-3x^2+9x+13#?

##### 1 Answer

Mar 5, 2016

Identify

#### Explanation:

First notice that reversing the signs of the coefficients of the terms with odd degree results in coefficients that sum to zero.

That is

So

#x^3-3x^2+9x+13#

#= (x+1)(x^2-4x+13)#

#=(x+1)(x^2-4x+4+9)#

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

#=(x+1)((x-2)-3i)((x-2)+3i)#

#=(x+1)(x-2-3i)(x-2+3i)#

So the zeros of