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A College Algebra Appendix Exam (A.3-A.6) Name Directions: You must show all work and reasoning to receive full credit. You work should be neat and well organized. Question 0) (1 point) What is the worst gift you ever received? Explain __________________________________________________________________________________________ __________________________________________________________________________________________ For Questions 1 – 3, answer True or False and explain your reasoning. 1) Synthetic Division can be performed on the following: 4 x 4 5 x3 9 x 10 x 2 1 . 2) 2 x 3 8 x3 27 3 3) The polynomial f ( x) x 2 5 x 7 has no real solutions. For Questions 4 – 8, factor completely. 4) x 2 3 x 54 5) 6 x 2 5 x 4 7) 4 x 3 20 x 2 3x 15 8) 12 x 2 x 1 3x 2 15 x 2 x 1 3 x 2 3 6) 8a 2 18b 2 4 2 5 A For Questions 9 and 10, simplify and give answer in fully factored, reduced form. State any restrictions on the variable. 22 −6 ( 2 ) +6−7 x2 4 9) 10) 62 −6−36 2x 3 x 3 ( 2 ) +9+14 For Questions 11 and 12, perform the indicated polynomial division. 11) synthetic division: 4 x4 12 x3 48x 61 x 4 12) long division: 6 x3 10 x2 x 8 2 x2 1 A For Questions 13 – 18, analytically solve the equations. Check your solutions on your calculator. 3 8 6 13) 14) 4(2 x 6)2 64 0 2 x 4 x 4 x 16 15) 4 x 2 x 2 16) 8 x 4 28 x3 16 x 2 0 17) 2 9 3x 12 0 18) x3 5x 2 4 x 20 For Questions 19 – 21, write the expression in the standard form a bi . 19) 2 i 7 4i 20) 3 2i 5 i 21) A 5 2i 2 3i For Questions 22 and 23, solve the equations in the complex number system. 22) 2 x5 10 x3 72 x 0 23) 2 x3 68x 16 x2