Oque é necessário para que um produto de fatores desconhecidos seja nulo?

What does it take for a product of unknown factors to be null?

No, you can only use synthetic division if you're dividing by something that looks like this:
x+b.

If the polynomial you're dividing by looks like this (for example):
2x+1
or this:
 2x^2 + x + 1

(these are all made up numbers, by the way, just examples)

then you cannot divide by it and muse therefore use long division