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in this lesson were going to focus on the rational zero theorem this theorem helps us to list all of the possible rational zeros of a polynomial function so its very useful when solving polynomial equations so heres an example lets say that f of x is equal to one x cubed plus two x squared minus five x minus six and lets list all of the possible rational zeros so we need to divide p by q and p is associated with the constant term q is associated with the leading coefficient so factors of p or factors of negative six include plus or minus one plus or minus two plus or minus three and plus a minus six now factors of the leading coefficient one is just plus or minus one and any number divided by one is itself so therefore the possible rational zeros are one two three and six so if we set this function equal to zero then the solutions to that equation will be sum of these numbers listed here so lets go ahead and do that so lets say that x cubed plus two x squared minus five x minus
