Chapter 2 Review Worksheet

Chapter 2 Review Worksheet

In 1-4, Sketch the graph of the given function by (a) applying the Leading Coefficient Test, (b) finding the zeros of the polynomial, (c) plotting sufficient points.

1. f(x) = −3x4 + 27x2 2. f(x) = x3 – 5x2

3. f(x) = 2x4 + 6x3 4. f(x) = x5 +3 x4 – 18x3

5. Use the process of completing the square to put the quadratic function into standard form: f(x) = 2x2 + 8x + 1.

6. List the possible rational zeros of f(x) = x3 – 2x4 + 3x + 25

7. Write the polynomial equation of least degree that has zeros of: −4, 1 –2i.

8. Solve: x4 – 6x2 – 40 = 0

In 9-14. Perform the indicated operation and write your answer in standard form.

9. (2i)2(3i) 10. (2 – 4i)(3 + 2i)

11. 12.

13. 14.

In 15-16, Sketch the graph of the given function by (a) applying the Leading Coefficient Test, (b) finding the zeros of the polynomial, (c) plotting sufficient points.

15. f(x) = x4 – 9x2 16. f(x) = x5 – x4 – 2x3

17. Use the process of completing the square to put the quadratic function into standard form: f(x) =

18. Write the polynomial equation of least degree that has zeros of: 2, i, 3 + i

19. Solve: x6 + 11x4 – 60x2 = 0

In 20-22, Write the polynomial as the product of linear factors with the given factor.

20. f(x) = x3 + 3x2 – 9x + 5; Given (x – 1) is a factor.

21. f(x) = x3 – 4x2 – 2x + 20; Given (x + 2) is a factor.

22. f(x) = x4 – 3x3 – x2 – 12x – 20; Given (x2 + 4) is a factor.

23. f(x) = x4 – 2x3 – 3x2 + 12x – 18; Given (x2 – 6) is a factor.

In 24-29, Perform the indicated operation and write your answer in standard form.

24. 25.

26. 27.

28. 29.

In 30-31, Write the polynomial function in standard form of the function graphed below.

30. The function pass through (−1, −4) 31. The function passes through (1, −6)

B