Rational Zeros Theorem Practice Test

Apply the Rational Zeros Theorem to help factor completely: $$P(x)=2x^3-9x^2+7x+6.$$ (Find a rational zero, factor it out, then factor the remaining quadratic.)

Possible rational zeros of $$P(x)=x^3-4x^2+x+6$$ are $\pm 1,\pm 2,\pm 3,\pm 6$. Which of these candidates are actual zeros? (You may test by substitution.)