# solve the rational polynomial equation

Week 5 Discussion Problems Identify any domain restrictions, the solve the rational polynomial equation. Check your work to verify your answers. 01) 02) 𝑥 2 −4 2𝑥 2 +3𝑥−2 =1 𝑥+1 𝑥+4 + 𝑥−1 𝑥+2 𝑥 2 +𝑥+1 = 𝑥 2 +𝑥−2 For the given polynomial function, a) State the leading term, leading coefficient, a, and degree, n. b) Describe the end behavior. c) Find the zeros and the multiplicity, m, of each. State whether the graph will cross the x-axis or rebound at each of the zeros. d) Create a sign chart by using test points for each interval. 03) 𝑓(𝑥) = 𝑥 2 (𝑥 − 3) 04) 𝑓(𝑥) = (𝑥 − 1)(𝑥 + 2)2 05) 𝑓(𝑥) = 2𝑥(𝑥 + 1)2 06) 𝑓(𝑥) = (𝑥 2 + 1)(3 − 𝑥) 07) 𝑓(𝑥) = (3𝑥 − 1)(𝑥 + 3)(𝑥 − 3) 08) 𝑓(𝑥) = 𝑥(2𝑥 − 1)2 (𝑥 − 3) 09) 𝑓(𝑥) = −2𝑥 4 (𝑥 − 1)2 10) 𝑓(𝑥) = (2𝑥 + 1)(𝑥 + 1)(𝑥 − 2)(2𝑥 − 1) Solve the rational inequality. Express your answer using interval notation. 11) 2𝑥 2 −𝑥−1 𝑥 2 −9 12) 3𝑥 2 −𝑥−2 3𝑥 2 +5𝑥+2 13) 4𝑥 2 −1 𝑥 2 +𝑥−6 14) 𝑥 2 −𝑥−2 𝑥 2 −6𝑥+8 0 ≤0
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