Is there a quick way to factor a fourth order polynomial WITHOUT a calculator?

Question

Say I was given the following polynomial:

x⁴+7x³+3x²+2

Is there a quick way to find the roots without using a calculator?

Answer 1

p/q gives you rational number possibilities. (rational root theorem)

p = factors of 2 and q = factors of 1

Then use synthetic division to find possibilities that are factors.

If you don't know how to do this, I am available for tutoring.