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
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