Rational Zeros Theorem Practice Test

A student claims that $x=\frac{3}{4}$ is a rational zero of $$P(x)=4x^3-11x^2-3x+18.$$ Use the Rational Zeros Theorem and/or direct testing to decide whether the claim is correct.

Use the Rational Zeros Theorem to help factor completely: $$P(x)=2x^3-3x^2-8x+12.$$ (Find a rational zero by testing candidates, divide to reduce the degree, and continue factoring.)