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Directions: For each question show all work that is required to arrive at the solution. Save this document with your answers and submit as an attachment to be graded.

Simplify each expression. Use positive exponents.

1. m3n–6p0

2.

a 4 b 3 ab 2

3. (x–2y–4x3) –2

4. Write the explicit formula that represents the geometric sequence -2, 8, -32, 128

5. Evaluate the function f (x) 4 • 7x for x 1 and x = 2. Show your work.

6. Simplify the quotient

4.5 x 103

9 x 107

.

Write your answer in scientific notation. Show your work.

Simplify the expressions. Show your work.

7. 3x(4x4 – 5x)

8. (5x4 – 3x3 + 6x) – ( 3x3 + 11x2 – 8x)

9. (x – 2) (3x-4)

10. (x + 6)2

Factor each expression. Show your work.

11. r2 + 12r + 27

12. g2 – 9

13. 2p3 + 6p2 + 3p + 9

Solve each quadratic equation. Show your work.

14. (2x – 1)(x + 7) = 0

15. x2 + 3x = 10

16. 4x2 = 100

17. Find the roots of the quadratic equation x2 – 8x = 9 by completing the square. Show your work.

18. Use the discriminant to find the number of real solutions of the equation 3x2 – 5x + 4 = 0. Show your work. A water balloon is tossed into the air with an upward velocity of 25 ft/s. Its height h(t) in ft after t seconds is given by the function h(t) = − 16t2 + 25t + 3. Show your work.

19. After how many seconds will the balloon hit the ground? (hint: Use the quadratic formula)

20. What will the height be at t = 1 second…...

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