Question

What are the possible rational zeros of f(x) = x4 + 2x3 − 3x2 − 4x + 12?

Answer 1

I believe it would be the first term over the last term, +/-, including the factors of both the last term, so:

for x^4:
1*4
2*2

for 12:
1*12
2*6
3*4

then divide all of this, and include the +/-'s of each. By divide, I mean take all the factors of the first term, aka the numerator, and those are possible rat. 0's. Then divide all those by the factors of the coefficient. Remove any duplicates.

Answer 2

The answer is plus or minus 1,2,3,4,6,12, those are the possible rational xeros and we can find this if we take the leading coefficient 1 from x^4 and the constant 12

We now could use our p/q

P would be your 12 and your q would be 1

Now find the factors of 12 and 1

p/q= 12/1= 1,2,3,4,6,12 /1 (all plus or minus)

possible rational zeros 1,2,3,4,6,12 (all plus or minus) :)