Name                          .

Math 152B Final

Please do all of the following problems.  All work and all answers must be done on your own paper.  Credit earned will be based on the steps that you show that lead to the final solution.  Good Luck!

Problem 1:  Factor the following

A)      x⁵y² - x³y⁴   

Solution

B)     6x² + 5x - 6   

Solution

C)     x³ + x² - 4x - 4 

Solution 

Problem 2:   Perform the indicated operations and simplify

A)       x³ + x² - 2x
                                   ÷  (x² + 2x)
               x - 1                                         

Solution

B)           10                   5
                              -                   
             h - 10              h - 5               

  Solution

Problem 3: Solve

A)   

Solution

B)   x³ + 2x² + x  =  0 

  Solution

Problem 4:  A motorboat travels 10 mi/hr in still water.  If the boat takes the same amount of time to travel 2 miles upstream as it does to travel 3 miles downstream, find the speed of the current.

  Solution

Problem 5:

A) Find the point of intersection of the two lines

        4x - 3y  =  15    and    5x - 6y  =  21

 Solution

B) Graph the solution set of

        7x + 2y  < 14

        3x - 5y  >  15

Solution

Problem 6: Simplify.  Write your answer without negative exponents.

  Solution

Problem 7:  Simplify

A)  

Solution

B)        2i + 1
                                   (Write your answer in the form a + bi)
            3 + 2i            

Solution

Problem 8:  Solve.  Any complex solutions should be written in the form a + bi.

A)    x² - 3x -15  =  0  

Solution

B)   2x² + 4  =  x   

Solution

C)    3x² - x - 1  =  0   

Solution

Problem 9  Complete the square

        2x² - 8x + 3  =  0

Solution

Problem 10  Use the discriminant to determine whether there are  two real roots,  two complex roots, or one real root.  Do not find the roots.

A.     2x² + 16x + 32 

Solution

B.     2x² - 5x - 10  

Solution

C.    12341234234x² - 3x + 12341324123123523

Solution

Problem 11  Answer the following true or false.  Please explain your reasoning.

1. If  c  <  0  then 
   
           x² + bx + c  =  0
   
   has two distinct real roots.
   
   Solution
   
   

2. If x = 2 and x = 4 is a solution of  |ax + b| < c , then x = 3 is also a solution.
   
   Solution

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