Question

Use the rational zeros theorem to list all possible rational zeros of the following:
h(x)= 4x^3-8x^2+6x+6

be sure that no value in your list appears more than once.

Answer 1

First try to guess some numbers to figure out at least one of root.

Answer 2

For example: x=2
lets check ..
4.8-8.4+6.2+6=18
so it's incorrect
try more to find a root
if a is a root then divide the poly equ to x-a
...

Answer 3

I have \[\pm1, \pm1/2,\pm1/4,\pm2,\pm3,\pm3/2,\pm3/4,\pm6\] is that what you right??

Answer 4

I think this method will do.
Let p = factors of the constant term which are \[(\pm 1, \pm2, \pm3, \pm6)\]
let q = factors of the leading coefficient which are \[( \pm 1, \pm2, \pm4)\]
To find the possible rational zeroes, let p/q = \[(\pm 1, \pm 2, \pm3, \pm6, \frac{ \pm1 }{ 2 },\frac{ \pm 3 }{ 2 }\frac{ \pm3 }{ 4 })\]
hence those are the possible rational zeroes