How do you use the rational roots theorem to find all possible zeros of #x^3-x^2-4x+4#?

1 Answer
Aug 20, 2016

Answer:

#color(green)(x in {-2, +1, +2})#
(see below for use of the Rational Root Theorem)

Explanation:

The Rational Root Theorem tells us that the rational zeros of

#color(red)(1)x^3-x^2-4x+color(blue)(4)#
are the factors of #(color(blue)(4))/(color(red)(1))#

Checking each of the possible factors we get:
enter image source here
which gives us zeros for

#x=-2, x=1, and x=2#

Since #x^3-x^2-4x+4# is of degree #3#
it can have a maximum of #3# zeros
and we have found them all.