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try 1, -1 first
then 2, -2
then 4,-4
if these don't work we have to move on to fractions

So what exactly is the textbook way for your textbook

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

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

well for this one i would guess -2

but its just a guess

x+2

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