POLYNOMIALS EXPONENTS AND LOGARITHMS. 1. Solve the following for x algebraically. a) log3 x log3 x 2 1 a)______________________________ 3 marks b) log5 7 x 1 log5 x log5 4 b)______________________________ 3 marks 2. Completely factor each of the following. Without the use of a calculator. Show all steps. No marks will be given for answers only. a) 15 x3 10 x 2 12 x 8 a)______________________________ b) x 4 13x 2 36 3 marks b)______________________________ 3 marks 3. Graph the polynomial f ( x) x 4 3 x3 4 x 2 3 x 2 using a Graphing Calculator. Sketch the graph in the window below and state the following: a) The Range b) The Real Zeros c) The y-intercept d) Relative Minimum and Relative Maximum e) The interval where f ( x) 0 a) _________________________ b) _________________________ c) _________________________ d) _________________________ [ , x mi x ma e) _________________________ [ , y mi yma 3 marks 4. On the graph provided, accurately sketch the given polynomial equation. Include the value of the zeros and y-intercept on your sketch. Draw with a smooth curve. f x x 1 x 4 x 1 2 y x 5. Express as a single logarithm. 3log A log B 2log C ____________________________ 6. . Solve for x . a) log x 81 4 3 a)______________________________ 2 marks b) 3log 4 x 6 b)______________________________ 2 marks c) 25 x 1 125 2x 1 c)______________________________ 2 marks 7. 1000 Write the expression in terms of log a and log b . log 4 a b 5.______________________________ 2 marks