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# preexam2sol - College Algebra/Analytic Geometry W1003...

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College Algebra/Analytic Geometry W1003 Section 003, Spring 2007 Exam 2, Thomas D. Peters Name: April 5, 2007 Do all problems, in any order. Show your work. An answer alone may not receive full credit. No notes, texts, or calculators may be used on this exam. Problem Possible Points Points Earned 1 20 2 10 3 10 4 10 5 10 6 20 7 10 8 10 TOTAL 80 1

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1. (20 points) Consider the polynomial P ( x ) = x 3 - 2 x 2 - 4 x + 8. (a)(5 points) Use the rational root theorem to list the possible rational roots of P ( note: you don’t need to check if they actually ARE roots). (b)(1 point) Show that 2 is a root of P . (c)(5 points) Compute P ( x ) x - 2 . (d)(2 points) Use your answer from (c) to factor P completely. (e)(2 points) What are the zeros of P and their respective multiplicities? (f)(5 points) Sketch the graph of P . Answer: (a) ± 8 , ± 4 , ± 2 , ± 1 (c) x 2 - 4 (d) P ( x ) = ( x - 2) 2 ( x + 2) (e) 2 (mulitplicity 2), -2 (multiplicity 1) 2. (10 points) Find the quotient and remainder using long division
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## This note was uploaded on 10/18/2011 for the course W 1003 taught by Professor Staff during the Spring '11 term at Columbia.

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preexam2sol - College Algebra/Analytic Geometry W1003...

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