Using rational zero theorem find all rational zeros

Question

P(x)=3x^3+43x^2+43x+27
Factors: 27, -1, 3, 9, 27
Factors: 3, -1, 3

+-1/3, +-1, +-3, +-9, +-27 possible rational zero for function P(x)

Answer 1

Is this correct?

Answer 2

Hmm I never heard of ration zero theorem but google says it involves synthetic division and checking for roots that make the equation equal to 0? Well, errm I hate synthetic division since it requires to much guess work >.< but all of the roots you wrote down are wrong according to my calculator.