Math 150 Test #2B NAME___________________________ Complete this test. When you have completed this test, submit your answers in the document Test #2B Submit Answers. Select the letter of the correct answer. 1. When completely factored, one of the binomial factors of 6x2 - 15x - 9 is: A) (x + 3) B) (2x + 1) C) (6x + 3) D) (3x - 9) 2. When completely factored, one of the binomial factors of 2ax + 3x + 4a + 6 is: A) (x + 3) B) 2(2a + 3) C) (2ax +3x) D) (x + 2) 3. Reduce the following to lowest terms: x x x 7 49 49 2 2 − − A) x x 7 + 7 B) − x − 7 1 C) 7x 1 − D) x x 7 7 + − 4. Reduce the following to lowest terms: 6 9 5 6 2 2 + + + + x x x x A) 3 2 + + x x B) 15 11 C) 3 6 + + x x D) x + 2 5. What values of x are NOT permitted in the following expression? ( 2)( )4 3 x − x + x A) x ≠ 0 B) x ≠-3 C) 4 x ≠ 2 and x ≠ − D) x ≠ -2 and x ≠ 4 6. Multiply and answer in lowest terms: x 3 4x 4x 4x x 4x 3 2 2 + + ⋅ + + A) (x2 + 3)(8x) B) (x + 1)2 C) ( )( ) 4x x 1 2x 2 2 − + D) (x+1)(x+3) 7. Divide and answer in lowest terms: 2 2 2 3a 4xy 9ax 8x y ÷ A) 3 2 3 27a 32x y B) 3 2 C) 3 2 3 a x y D) 3y a2 8. Combine and Simplify: x x 2 3 5 − − A) ( )3 (3 )2 − + x x x B) ( )3 3 x x − C) ( )3 3 6 − − x x x D) -1 9. Simplify (express answer in lowest terms): y xy y xy x 1 1 1 − + A) 1 1 2 − + x x B) x + 1 C) x - 1 D) x 10. Solve for x: 2 3 1 2 3 + = x x x = A) 5 2 B) 3 1 C) 12 11 D) 11 2 11. Solve for x: a(x – 3) = b(2x – 1) x = A) ab 1 − B) a b a b 2 3 − − C) ab a b 2 3 − − D) 2 3 − 12. Solve for a: 2 0 at 2 1 s = v t + a = A) 2 o -s2 2v t t B) t -s2 2vo C) 2 o 2s- v t t D) 2 o 2 1 -s v t − t 13. Factor completely: 8a3 + b3 A) (2a + b)3 B) (2a + b)(4a2 – 4ab + b2 ) C) (2a + b)(4a2 – 2ab + b2 ) D) (2a – b)(2a2 + b2 ) Part II: For each of the following problems, show your work. Work must be shown to receive credit. To show your work, answer each part. When typing your work make sure you label the parts in the problem, a, b etc. 14. Divide and answer in lowest terms: 3x 3x x 9 3x 3x 3x 8x 3 2 2 2 2 + − ÷ − − − a) When completely factored, the factors of the first numerator are: b) When completely factored, the factors of the first denominator are: c) When completely factored, the factors of the second numerator are: d) When completely factored, the factors of the second denominator are: e) Your final answer in lowest terms is: 15. Combine and answer in lowest terms: x 1 2 x 3x 2 3 2 2 − − + + a) What is the LCD: b) Type out some steps of your work. c) Your final answer in lowest terms is: 16. Solve for x: x 2x 3 2x 5 x 1 4 x 3 5 2 + − + − − = + a) What is the LCD b) Explain your procedure for solving this problem and type out a few steps of your work. c) Your final answer is: 17. An oil tank is being filled by two pipes. One pipe working alone could fill the pipe in 18 hours. The second pipe working alone could fill the tank in 15 hours. How long will it take to fill the tank using the two pipes at the same time? a) State what your variable represents. b) Write an equation to solve this problem. c) Solve your equation showing your work. 

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