Use the Rational Zeros Theorem to generate a list of potential rational zeros

1. Let p(x) = 3x
5 + 3x
4 − 6x
3 − 15x
2 − 15x − 6.
(a) Use the Rational Zeros Theorem to generate a list of potential rational zeros.
(b) Use Descartes’ Rule of Signs to find the possible number of positive and negative real zeros.
(c) Find all real zeros of p and state their multiplicities.
(d) Sketch the graph of y = p(x). Be sure find:
i. the y-intercept
ii. the end behavior
iii. the x-intercepts
2. Solve: 2x
3 + 3 ≥ x
2 + 4x.

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