Problema Solution

List all possible (or potential) rational zeros for the polynomial below. Find all real zeros of the polynomial below and factor completely over the real numbers. Please show all of your work.

f(x)=3x^3+14x^2+x-2

Answer provided by our tutors

f(x)=3x^3+14x^2+x-2

There are 1 sign changes in the "positive" case. This number "1" is the maximum possible number of positive zeroes

f(-x)=-3x^3+14x^2-x-2

There are 2 sign changes in the "negative" case.  This number "1" is the maximum possible number of negative zeroes