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Please show all work Factor out the GCF in each expression. 65 12x4t + 30x3t + 24x2t 66 15x2y2 - 9xy2 + 6x2y Factor each polynomial completely. 55 3x2 + 6x + 3 56 12a2 + 36a + 27 72 x3 + x2 - x - 1 73 3a – 3b – xa + xb Factor each polynomial. 62 h2 – 9hs + 9s2 82 9w - w3 = w (9 - w2) 97 8vw2 + 32vw + 32v Factor each trinomial using trial and error. 55 15x2 – x – 2 56 15x2 + 13x – 2 Factor this polynomial completely. 91 2x2y2 + xy2 + 3y2 Factor this polynomial completely. 53 9x2 + 6x + 1 54 9x2 + 6x + 3 Solve each equation. 7 (x + 5)(x + 4) = 0 10 (3k – 8)(4k + 3) = 0 16 q2 + 3q – 18 = 0 18 2h2 – h – 3 = 0 51 3x2 + 15x + 18 = 0 57 (x – 2)2 + x2 = 10 ___________________ Next _____________________ Please show your complete work in each question. Find the GCF for each group 1 12 a2b 18 ab2 24a3b 3 45m2n5 2 56a4b 8 Factor each polynomial completely 3 a2 2a 24 4 3m3 27m 5 ax 2a 5x 10 6 8a2 40ab 50b2 7 m2 4mn 4n2 8 3x 3 y2 3x2 y2 3xy2 Solve each equation 9 2x 2 5x 12 0 10 (x 3)2 (x 2)2 17 Write a complete solution including all the steps to each of the following problems: 11 The sum of two numbers is 4 and their product is -32 Find the numbers. Let’s revisit Mike’s front yard of last week’s lecture. This week, Mike would like to plant some trees so he needs to use a portion of his existing 12 yard. The perimeter of this rectangular portion needs to be 14 yards and the diagonal is 5 yards. Can you help Mike determine the length and width of this new portion? Mike requested that you show him how you arrive at the answers, so please show your complete work. 13 Do you remember Little Johnny from last week’s lecture? He now wants to invest further using $16000 that he has saved. The investment grew up to $25000 in 2 years. Can you find the annual interest rate of his return by solving the following equation for him: 16000(1 + x)2 = 25000 14 Remember the calculation of response time in the lecture? R = SQ + S (2) Based on one Queuing Theorem: Q = a*R (3) Manipulating equations (2) and (3) using Factoring method, we obtain: S R = ---------1–aS (4) Show how you manipulate the two equations (2) and (3) in order to get (4). Part 2. In a study of worker productivity at The Sanford Company, it was found that the number of components assembled per hour by the average worker t hours after starting work could be modeled by the function: (10 pts) f(t) 3t 3 23t2 8t a. Rewrite the formula by factoring the right-hand side completely. b. Use the factored version of the formula to find f(3) c. Use the following graph to estimate the time at which the worker are most productive. Where is the point of diminishing return? d. Use the below graph to estimate the maximum of components assembled per hour during an 8-hour-shift. Note: Graph was drawn for illustration purposes using approximate measurements. # Components Productivity 300 200 100 0 0 2 4 6 Hours 8 10