Rational Zero's Theorom?

Question

Can someone please explain the Rational Zero's Theorem in further detail?

Answer 1

zeros are solutions to an equation or x-intercepts of a graph (if they are real and not imaginary, of course....). you can find a list of possible rational zeros by dividing all the factors of the a function's constant over all the factors of the leading coefficient. for example....

f(x) = 4x^5 + 2x^4 + .......... + 2

the list of possible zeros would be factors of 2 over factors of 4....

+/- 1, 2
-----------
+/- 1, 2, 4

= +/- 1, 2, 1/2, 1/4 (i'm trying to show that you have to check the positive and negative of each # listed)

put all of these into synthetic division and if one has zero for a remainder, then it is "a zero".

of course, once you get find enough zeros to knock the polynomial down to a quadratic (2nd degree), then quit this ridiculous synthetic division chase and just factor or quadratic formula it to find the last 2 zeros.

good luck.