Beginning Algebra Review Exam 3


Material covered:

    Adding and Subtraction Polynomials
    Multiplying Polynomials
    Dividing Polynomials
    Factoring Polynomials
    Solving Quadratic Equations By Factoring

I.  Polynomials:  Perform the indicated operations.

    A.   1.  (3x² - 5x + 4) + (7x² + 9x - 8)

         2.  (7x² - 5x + 3) - (-2x² + 6x - 4)

         3.  5x(x - 4) - 3x(2x + 1)

         4.  (6x² y)(4x³ y² )

         5.  (3x - 8)(4x + 1)

         6.  (2x²  + 3x - 1)(x²  + 5x + 4)

         7.  (4a³ )²

         8.  (5x - 3)²

         9.  (5x³ y³ )/(xy² )

         10.  (14x³  - 22x)/(2x)

         11.  (2x³ + x - 4)/(x - 2)

    B.   1.  Subtract x²  + 4x - 3 from 2x²  + 7x - 8.

         2.  What is the degree of the polynomial 4x²  + 7x³  - 3x  +  9 ?

II. Factoring.

    A.  Completely factor.

         1.  3x²  - 9x - 30

         2.  6x²  - 7x - 10

         3.  50x²  - 32

         4.  49x²  - 42x + 9

         5.  x²  - 5x  - 36

         6.  125x³ - 64

         7.  27x³ + 8

     B.  Solve for x.

         1.  2x²  - 3 = -5x

         2.  4x²  - 20x + 25 = 0

         3.  5x²  + 6x - 8 = 0

    C.  Stated Problems.

         1.  The base of a triangle is four feet shorter than twice its altitude.  If the area
             of the triangle is 48 square feet, find its dimensions.

         2.  The base of a triangle is four feet shorter than twice its altitude.  If the area
             of the triangle is 48 square feet, find its dimensions.

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