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

1 Answer
Nov 22, 2016

Answer:

All possible rational zeros are #-3#, #-1# and #1#.

Explanation:

If #a#, #b# and #c# are zeros of a polynomial of degree #3# in #x#, then the function is #(x-a)(x-b)(x-c)#. Hence let us factorize #x^3+3x^2-x-3#

#f(x)=x^3+3x^2-x-3#

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

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

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

Hence, all possible rational zeros are #-3#, #-1# and #1#.