Lesson College Algebra Exam Polynomial Equations and Functions, Systems of Equations and Inequalities

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COLLEGE ALGEBRA EXAM 3 CG R² NAME __________________

SHOW ALL WORK ON THIS TEST OR ON SEPARATE PAPER. Circle answers.

TURN IN ALL WORKSHEETS. CALCULATORS ARE REQUIRED ON THIS TEST.

1. Solve the systems of equations:

a) 50x – 9y = 1 b) y = 2x – 4

7x – 2y = – 8 4x – 2y = 8

2. Solve the system: 3. Solve the system:

3x + 2y + 5z = 2 3x + 2y = – 2

2x – 3y + 2z = – 4 2y – 3z = 1

x + 4 + 2z = 2 x – 2y + 2z = 4

4.    Solve the system:                                                         5.     Solve the system:

        y² – 4x² = 105                                                                              xy = – 12

        y = 3x – 5                                                                                2x – y = – 11

6. Evaluate the determinants:

   a)                                    b)

7. Evaluate the determinant:



8. Solve by Cramer's Rule:              9. Graph the intersection:

         x – 2y = 8                                      x ³ 0

     –8x + 6y = 32                                    2x – 3y ³ 12

                                                                  7x + 4y > 28





10. Find the remainder if x⁷ – 6 x² + 3 is divided by x – 1.

11. Find a quadratic equation whose roots are x = 5 ± 3i.



12. Solve for x. Give irrational roots in radical form:

         x⁴ – x³ – 2 x² + x + 1 = 0





In 13 - 14, find all roots and multiplicities by synthetic division:

13.    x³ + x² – 8 x – 12 = 0                             14.   x⁴ – 5 x³ + x² + 21 x – 18 = 0



In 15 - 16, sketch the graphs and give roots:

15.    y = (x – 2)³(x + 3)²(x – 4)                       16.     y = x³ + 2 x² – 4 x – 8



In 17 - 20, solve the inequalities. Give interval notation.

                  Sketch graphs when using graphing methods.

17. | x + 8 | ≥ 6                                             18.     –7x² + 40x > –12      (Give exact form!)



19.                                                       20.



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