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

-1, -1, -1/3, 2 = answer to Part B

are the "four" zeros

or just "three" if you don't count the -1 twice

graph the equation and find the x intercepts = the zeros = the roots

if the graph is tangent to the x axis then the zero repeats

or factor and set each factor =0, then solve for x to get the zeros

3x^4 + x^3 -9x^2 -9x -2

=3(x-2)(x+1/3)(x+1)(x+1)

=(x-2)(3x+1)(x+1)^2

or do integer factors of the constant term over integer factors of the coefficient of the highest degreed term, and try them all and see which ones work. trial and error method. try plus or minus 2/3, 1/3, 1/1, 2/1 = the Answer to Part A

Answer 2

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 3

Read the Rational Root Theorem.

Did you look at the graph for the zeros?