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Alg 2 BC U6 Quiz Review (Day 6) Give the end behavior of each polynomial function: 1. y (3 x)( x 5)2 ( x 1)3 3. Divide WITHOUT a calculator: 2. y 25 x 4 3x 23 (4 x5 3x3 7 x 4) (2 x 3) 4. WITHOUT a calculator, graph each polynomial. Use x-intercepts (including the concept of MULTIPLICITY, y-intercepts and end behavior.) (For irrational zeros, approximate the radical by determining the two integers that it lies between.) a) y (3 x)( x 5)2 b) y x 4 2 x3 x 2 c) y x3 8 x 2 16 x 5 d) y x 4 5x 2 36 5. If (Hint: -5 is one of the zeros.) f ( x) 5x5 ax 2 7 x 2 , for what value of "a" does f(3)=27? (Use synthetic substitution to solve.) 6. Classify the polynomials in 4c and 4d by DEGREE and NUMBER OF TERMS. 7. Factor: a) 125 x12 1 b) 4 x4 109 x2 225 8. Solve each polynomial equation. The number of solutions should equal the degree of your highest term. a) 64 y3 125 c) 2 x3 10 x 7 x 2 35 b) x 4 2 x 2 5 d) (Yes, these are complicated answers.) 12 x3 61x2 x 30 (One solution is 3/4.) 9. Write a polynomial equation IN STANDARD form with zeros -3 (multiplicity 2) and 4 (multiplicity 1.) 10. CALCULATOR OK: A box has dimensions 8 inches x 12 inches x 25 inches. The same number of inches is ADDED to the two shorter dimensions and SUBTRACTED from the largest dimension. If "x" represents the number in inches added/subtracted, write a polynomial expressing the volume of the new box. Then, use the "Calc maximum" on your calculator to find the number of inches that should be added/subtracted in order to maximize the volume of the new box, as well as the maximum volume (all to the nearest thousandth.) HINT: Start with a window of -20/20/1 -100/100/1. Then use your understanding of polynomials to get to the window that you need to answer the question.