A+ Answers

Factor COMPLETELY when possible. If the polynomial is prime, say so.

1.         X² – 3XY – 54Y²

2.         81a² + 4b²

3.         10M⁴ – 25M² + 20MN

4.         28X³ + 8X² + 49X + 14

5.         8X² + 17X – 21

6.         10Y² + 11Y – 6

7.         6T² + 5ST – 6S²

8.         64X³ – 27Y³

Solve each equation for the given variable.

9.         y(5y + 13) = 6

10.       4T² – 32T + 60 = 0

11.       X³ + 6X² – X – 6 = 0

12.       4X(X + 2) = (3X – 3)(X + 2)

Solve the following problems.

13.       The length of a rectangular storage room floor is 5 feet longer than its width. If   the area of the floor is 66 square feet, find its dimensions.

14.       If h = -16t² + 192t represents the height of a firework, in feet, t seconds after it             was fired, when will the firework be 576 feet high?

15.       A manufacturer determines that the profit in dollars for manufacturing n units is

            P = 2n² – 70n + 20. Assume n is a positive integer. How many units must be

            produced to create a profit of $420?

16.       Find the domain of  

Simplify each rational expression:

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Add or subtract:

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24.        

Solve each rational equation

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27.        

Simplify the expression

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31.        

Rationalize the denominator in each expression below

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35.       Graph the function by hand. Make your own grid below.

36.        

                        Plot the points (0, 4), (3, 5), (8, 6), and (-1, 3) and draw a smooth curve                            through the points.

Solve each equation

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40. Sketch the graph of the function.  

            Plot the points (4, -10), (5, -4), (6, -2), (7, -4), and (8, -10) 

41.       Sketch the graph of the function.  

            Plot the points (-4, -5), (-3, 0), (-1, 4), (1, 0), and (2, -5).

42.       Find an equation of the function sketched below in the form:

43.       Sketch by hand the graph of the function. Give the coordinates for the vertes.

44.       A developer wants to enclose a rectangular grassy lot that borders a city street for             parking. If the developer has 280 feet of fencing and does not fence along the

            street, what is the largest area that can be enclosed?

45.       Solve: (2x + 5)² = 6

46.       Solve:   

47.       Solve by completing the square:         

48.       Solve by completing the square:         

49.       Solve using the quadratic formula:     

50.       Solve using the quadratic formula: