Question

Find any rational roots of P(x).
P(x)=3x^4+2x^3-9x^2+4

Answer 1

try 1, -1 first
then 2, -2
then 4,-4

if these don't work we have to move on to fractions

Answer 2

there is more than 1 so even if they work there wtill might be a fraction. Oh and with this i have to show my work and do it the textbook way not by trial and error

Answer 3

So what exactly is the textbook way for your textbook

Answer 4

there is no other way to do it
you have to check. if that is "trial and error' that is what you need to do

Answer 5

Well, in practicality my teacher told me to graph the function.. and then you can use synthetic division for the ones that aren't "exact"

Answer 6

But unless you have some sort of sixth sense of math you really don't have a set method.. unless your textbook does, in which case i'd want to know.

Answer 7

ya thats the way i am just having trouble relating it to this specifc problem

Answer 8

1 works by your eyeballs because if
\[P(x)=3x^4+2x^3-9x^2+4\] then \[P(1)=3+2-9+4=0\]

Answer 9

well for this one i would guess -2

Answer 10

but its just a guess

Answer 11

add up the coefficients and see that you get 0
then you can factor as
\[(x-1)\times (something)\] and then you can either factor the "something" or else use the quadratic formula

Answer 12

you only need to find one zero, then factor and end up with a quadratic, and you can always find the zeros of any quadratic

Answer 13

scratch that, this is a polynomial of degree 4, so you factor and end up with a cubic
when you do that, you will see that 1 is a zero of the cubic polynomial as well, so you will factor again as \((x-1)(x-1)(something)\)

Answer 14

x+2

Answer 15

but there really isn't an exact method to it is all.