ALG



ALG. 2 CH. 5 POLYNOMALS PREVIEW

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Classify –3x5 – 2x3 by degree and by number of terms.

|a. |quintic binomial |c. |quintic trinomial |

|b. |quartic binomial |d. |quartic trinomial |

____ 2. Zach wrote the formula w(w – 1)(4w + 2) for the volume of a rectangular prism he is designing, with width w, which is always has a positive value greater than 1. Find the product and then classify this polynomial by degree and by number of terms.

|a. |[pic]; quintic trinomial |

|b. |[pic]; quartic trinomial |

|c. |[pic]; quadratic monomial |

|d. |[pic]; cubic trinomial |

____ 3. Write 3x2(5x2 + x3) in standard form. Then classify it by degree and number of terms.

|a. |8x + 4x4; quintic binomial |c. |3x5 + 5x4; quartic binomial |

|b. |3x5 + 15x4; quintic binomial |d. |8x5 + 15x4; quintic trinomial |

____ 4. Use a graphing calculator to determine which type of model best fits the values in the table.

|x |–6 |–2 |0 |2 |6 |

|y |90 |14 |0 |2 |54 |

|a. |linear model |c. |cubic model |

|b. |quadratic model |d. |none of these |

____ 5. The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1995. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 2006.

|Years since 1995 |1 |3 |5 |7 |9 |

|Trees planted (in thousands) |1.3 |18.3 |70.5 |177.1 |357.3 |

|a. |[pic]; 630.3 thousand trees |

|b. |[pic]; 630.3 thousand trees |

|c. |[pic]; 618.1 thousand trees |

|d. |[pic]; 618.1 thousand trees |

____ 6. The table shows the number of llamas born on llama ranches worldwide since 1988. Find a cubic function to model the data and use it to estimate the number of births in 1999.

|Years since 1988 |1 |3 |5 |7 |9 |

|Llamas born (in thousands) |1.6 |20 |79.2 |203.2 |416 |

|a. |[pic]; 741,600 llamas |

|b. |[pic]; 563,200 llamas |

|c. |[pic]; 741,600 llamas |

|d. |[pic]; 563,200 llamas |

____ 7. Write 3x3 + 9x2 – 54x in factored form.

|a. |3x(x + 6)(x – 3) |c. |3x(x – 3)(x – 6) |

|b. |6x(x – 3)(x + 3) |d. |–3x(x + 3)(x + 6) |

____ 8. Miguel is designing shipping boxes that are rectangular prisms. One shape of box with height h in feet, has a volume defined by the function [pic]. Graph the function. What is the maximum volume for the domain [pic]? Round to the nearest cubic foot.

|a. |47 ft3 |b. |8 ft3 |c. |56 ft3 |d. |49 ft3 |

____ 9. Use a graphing calculator to find the relative minimum, relative maximum, and zeros of [pic]. If necessary, round to the nearest hundredth.

|a. |relative minimum: (–62.24, 0.36), relative maximum: (37.79, –3.69), |

| |zeros: x = 5, –2, 2 |

|b. |relative minimum: (0.36, –62.24), relative maximum: (–3.69, 37.79), |

| |zeros: x = –5, –2, 2 |

|c. |relative minimum: (0.36, –62.24), relative maximum: (–3.69, 37.79), |

| |zeros: x = 5, –2 |

|d. |relative minimum: (–62.24, 0.36), relative maximum: (37.79, –3.69), |

| |zeros: x = –5, –2 |

____ 10. Find the zeros of [pic]. Then graph the equation.

|a. |0, –5, –4 |c. |–5, –4 |

| |[pic] | |[pic] |

|b. |–5, –4, 5 |d. |0, 5, 4 |

| |[pic] | |[pic] |

____ 11. Determine which binomial is not a factor of [pic].

|a. |x + 4 |c. |x – 5 |

|b. |x + 3 |d. |4x + 3 |

____ 12. Determine which binomial is a factor of [pic].

|a. |x – 12 |b. |x – 13 |c. |x – 4 |d. |x + 4 |

____ 13. The volume of a shipping box in cubic feet can be expressed as the polynomial [pic]. Each dimension of the box can be expressed as a linear expression with integer coefficients. Which expression could represent one of the three dimensions of the box?

|a. |x + 6 |c. |2x + 3 |

|b. |x + 1 |d. |2x + 1 |

____ 14. The dimensions in inches of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and height 3x – 1. The volume is about 7.6 ft3. Find the dimensions of the box in inches. Round to the nearest inch.

|a. |15 in. by 20 in. by 44 in. |c. |15 in. by 20 in. by 45 in. |

|b. |12 in. by 17 in. by 35 in. |d. |12 in. by 17 in. by 36 in. |

Short Answer

Factor the expression.

15. [pic]

16. [pic]

17. [pic]

Solve the equation by graphing.

18. [pic]

19. [pic]

20. Use synthetic division to find P(–1) for [pic].

Divide using synthetic division.

21. [pic]

22. [pic]

23. Divide [pic] by x + 2.

24. Find the zeros of [pic] and state the multiplicity.

25. Write a polynomial function in standard form with zeros at –3, 5, and 2.

26. Write the expression (x + 5)(x + 3) as a polynomial in standard form.

27. Classify 9x5 – 5x3 + 7x2 + 7 by degree and by number of terms.

28. Write the polynomial [pic] in standard form.

29. Use a graphing calculator to find a polynomial function to model the data.

|x |1 |2 |3 |4 |5 |6 |7 |8 |9 |10 |

|f(x) |12 |4 |5 |13 |9 |16 |19 |16 |24 |43 |

ALG. 2 CH. 6 POLYNOMALS PREVIEW

Answer Section

MULTIPLE CHOICE

1. ANS: A

2. ANS: D

3. ANS: B

4. ANS: B

5. ANS: B

6. ANS: C

7. ANS: A

9. ANS: B

10. ANS: A

11. ANS: A

12. ANS: C

13. ANS: D

14. ANS: A

SHORT ANSWER

15. ANS:

[pic]

16. ANS:

[pic]

17. ANS:

3

18. ANS:

no solution

19. ANS:

0, –1.4, 0.4

20. ANS:

13

21. ANS:

[pic], R –38

22. ANS:

[pic]1

23. ANS:

[pic], R –22

24. ANS:

3, multiplicity 6; –2, multiplicity 2

25. ANS:

[pic]

26. ANS:

x2 + 8x + 15

27. ANS:

quintic polynomial of 4 terms

28. ANS:

[pic]

29. ANS:

f(x) = 0.08x4 – 1.73x3 + 12.67x2 – 34.68x + 35.58

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download