Question

Review for Sections 3.2 and 3.3:

1. [3 pts] Use synthetic division to divide x5 – x4 – 3x3 – 4x2 + 2x – 51 by x – 3. (Show algebraic work.)









2. [4 pts] Solve the equation x3 – 11x2 + 38x – 40 = 0 given that 4 is a zero of f (x) = x3 – 11x2 + 38x – 40. (Show algebraic work.)








3. [5 pts] Answer parts a. – c. below for the given polynomial function: f (x) = 4(x – 2)5(x – 3)2(x + 5)

a. What are the zeros of this polynomial function?



b. Give the multiplicity of each zero.

  


c. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero.   




4. [6 points] Answer parts a. – c. below for the following graph.

a. Find the zeros and state whether the multiplicity of each zero is even or odd.



b. Using the zeros and multiplicity values found in part a., write an equation, expressed as the product of factors, of the graphed polynomial function. (Make the degree of f as small as possible.)





c. Using your equation in part b., find the y-intercept of the graph. (Show algebraic work.)




5. Answer parts a. – f. below for the given polynomial function: f (x) = x3 – x2 – 9x + 9

[2 pts] a. Using the leading coefficient test, determine the graphs end behavior.

  

[3 pts] b. Find the x-intercepts. (Show algebraic work.)








[2 pts] c. For each of the x-intercepts found in part b., state whether the graph crosses the x-axis, or touches the x-axis and turns around at this intercept.   





[1 pt] d. Find the y-intercept.   





[1 pt] e. Determine the maximum number of turning points.






[3 pts] f. Using the information found in parts a. – e., graph the polynomial function.