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prereview2 - Precalc Review Problems for Second Exam This...

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Precalc Review Problems for Second Exam This practice exam is longer than the actual exam will be–the actual exam will consist of roughly 100 points of similar problems to those listed below. Please leave all answers in ex- act form–involving e , ln, log, etc. No calculators are necessary or will be allowed on the exam. 1. (15 points) Sketch the graph of the polynomial function. Mark all intercepts. (a) P ( x ) = (2 x - 1)( x + 1)( x + 3) (b) P ( x ) = x 6 - 2 x 3 + 1 2. (10 points) Find the quotient and remainder using synthetic division x 4 - x 3 + x 2 - x + 2 x - 2 3. (10 points) Find the quotiend and remainder using long division 3 x 4 - 5 x 3 - 20 x - 5 x 2 + x + 3 4. (10 points) Find a polynomial of degree 4 with integer coefficients and zeros 1, -1, 2, and 1 2 . 5. (10 points) Find all rational zeros of the polynomial P ( x ) = x 3 + 3 x 2 - 4. 6. (15 points) Perform the complex arithmetic (a) (2 + 5 i ) + (4 - 6 i ) (b) i 1003 (c) 1 1 - i - 1 1 + i 7. (10 points) Find all solutions of the quadratic equation 2 x 2 + 3 = 2 x .
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