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Math 152B Midterm I

Please do all of the following problems.  Credit earned will be based on the steps that you show that lead to the final solution.  Good Luck!

Problem 1:  Factor the expression completely:

A)   x⁴ - 9x² Solution

B)    x² + 3x - 54 Solution

C)    6x² + 11x - 10 Solution

D)    128xyz³ + 54x⁴y Solution

Problem 2:  Perform the indicated operations and express your answer in simplest form.

A       2x² - x - 1     x² - 6x + 8
                           ^.                            Solution                
         x² - 5x + 4    2x² - 3x -2

B       x² + 2 xy + y²           y + x
                                                 Solution            
          x² - x - 2                x - 2

Problem 3:  Solve the following equations

A.   x³ - 2x² + x = 0 Solution

B.    4x² = 15 - 4x Solution

Problem 4:  Solve the following inequalities

A.     |4 - 3x|  < 2 Solution

B.  |3x + 1| < 0 Solution

Problem 5:  There is a lookout post situated in the center of a 3 mile circular trail.  How far is the lookout post from the trail? Solution

Problem 6:  Please answer the following true or false and explain your reasoning.

A.  If all terms of a trinomial are positive, all terms of both binomial factors will be positive  Solution

B.  The solution to the inequality |x - 4|  <  -1 is the interval [3,5]. Solution

Extra Credit:  Write down one thing that your instructor can do to make the class better.

(Any constructive remark will be worth full credit)

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