Question

What is the Rational Zeros Theorem? How can i apply it to something like this[ f(x) = 3x^3 + 39x^2 + 39x + 27 ] ?

Answer 1

The rational root theorem is when you take all of the factors of the constant of a polynomial (usually labeled p) and put it over all possible factors of a or the leading coefficient (usually labeled q). Therefore, \(\LARGE\frac {±p}{±q}\). THis gives you the possible rational roots. It is usually used hand in hand with Descartes Rules of Signs. So for this one, all possible roots are:
\[±\frac13, ±1, ±3, ±9, ±27\]