Rational Zero Theorem | Find all rational zeros of polynomial function synthetic division

In this example, we use the rational zero theorem to list all the possible rational zeros. Then we test possibilities using synthetic division until we find one that gives a remainder of zero. We use that divisor to rewrite the original polynomial as the divisor multiplied by the quotient. The quotient (a quadratic) is then factored completely. From the resulting factors, we list out each zero of the original polynomial function.