need help solving this

Question

A polynomial function P and its graph are given.

P(x) = 3x4 + x3 − 9x2 − 9x − 2

A. List all possible rational zeros of P given by the Rational Zeros Theorem. (Enter your answers as a comma-separated list.)

B. From the graph, determine which of the possible rational zeros actually turn out to be zeros. (Enter your answers as a comma-separated list. Enter all answers using the appropriate multiplicities.)

Answer 1

A. P(x) = 3x⁴ + x³ − 9x² − 9x − 2;

±1. ±2 are devisers of -2;

±1, ±3 are devisers of 3

So, by Rational Zeros Theorem Possible rational zeros: ±1, ±2, ±1/3, ±2/3

B. We have graph by RI-84 and get -1/3, -1, -1 and 2

Answer 2

Read the Rational Root Theorem.

Did you look at the graph for the zeros?