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ALG. 2 CH. 6 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. Classify –7x5 – 6x4 + 4x3 by degree and by number of terms.

|a. |quartic trinomial |c. |cubic binomial |

|b. |quintic trinomial |d. |quadratic binomial |

____ 3. Zach wrote the formula w(w – 1)(5w + 4) 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]; quadratic monomial |

|c. |[pic]; cubic trinomial |

|d. |[pic]; quartic trinomial |

____ 4. Write the polynomial [pic] in standard form.

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 5. Write 4x2(–2x2 + 5x3) in standard form. Then classify it by degree and number of terms.

|a. |2x + 9x4; quintic binomial |c. |2x5 – 8x4; quintic trinomial |

|b. |20x5 – 8x4; quintic binomial |d. |20x5 – 10x4; quartic binomial |

____ 6. Use a graphing calculator to determine which type of model best fits the values in the table.

|x |–6 |–2 |0 |2 |6 |

|y |–6 |–2 |0 |2 |6 |

|a. |quadratic model |c. |linear model |

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

____ 7. 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 |

|a. |f(x) = 0.8x4 – 1.73x3 + 12.67x2 – 34.68x + 35.58 |

|b. |f(x) = 0.08x3 – 1.73x2 + 12.67x + 35.58 |

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

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

____ 8. 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 |

____ 9. 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 |

____ 10. Write the expression (x + 6)(x – 4) as a polynomial in standard form.

|a. |x2 – 10x + 2 |c. |x2 + 2x – 24 |

|b. |x2 + 10x – 24 |d. |x2 + 10x – 10 |

____ 11. Write 4x3 + 8x2 – 96x in factored form.

|a. |6x(x + 4)(x – 4) |c. |4x(x + 6)(x + 4) |

|b. |4x(x – 4)(x + 6) |d. |–4x(x + 6)(x + 4) |

____ 12. 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. |10 ft3 |b. |107 ft3 |c. |105 ft3 |d. |110 ft3 |

____ 13. 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 |

____ 14. Find the zeros of [pic]. Then graph the equation.

|a.|3, 2, –3 |c.|3, 2 |

| |[pic] | |[pic] |

|b.|0, –3, –2 |d.|0, 3, 2 |

| |[pic] | |[pic] |

____ 15. Write a polynomial function in standard form with zeros at 5, –4, and 1.

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 16. Find the zeros of [pic] and state the multiplicity.

|a. |2, multiplicity –3; 5, multiplicity 6 |

|b. |–3, multiplicity 2; 6, multiplicity 5 |

|c. |–3, multiplicity 2; 5, multiplicity 6 |

|d. |2, multiplicity –3; 6, multiplicity 5 |

____ 17. Divide [pic] by x + 3.

|a. |[pic] |c. |[pic] |

|b. |[pic], R –93 |d. |[pic], R 99 |

____ 18. Determine which binomial is not a factor of [pic].

|a. |x + 4 |c. |x – 5 |

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

____ 19. Determine which binomial is a factor of [pic].

|a. |x + 5 |b. |x + 20 |c. |x – 24 |d. |x – 5 |

____ 20. 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 |

Divide using synthetic division.

____ 21. [pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 22. [pic]

|a. |[pic], R 70 |c. |[pic], R 46 |

|b. |[pic], R –62 |d. |[pic], R –38 |

____ 23. Use synthetic division to find P(2) for [pic].

|a. |2 |b. |28 |c. |4 |d. |–16 |

Solve the equation by graphing.

____ 24. [pic]

|a. |x = 49 |b. |no solution |c. |x = 19 |d. |x = 12 |

____ 25. [pic]

|a. |no solution |c. |0, 2, –0.38 |

|b. |–2, 0.38 |d. |0, –2, 0.38 |

____ 26. [pic]

|a. |3 |b. |–3 |c. |–3, 3 |d. |no solution |

____ 27. 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. |

Factor the expression.

____ 28. [pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 29. [pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 30. Solve [pic]. Find all complex roots.

|a. |[pic], [pic] |c. |[pic],[pic] |

|b. |no solution |d. |[pic], [pic] |

ALG. 2 CH. 6 POLYNOMALS PREVIEW

Answer Section

MULTIPLE CHOICE

1. ANS: A

2. ANS: B

3. ANS: C

4. ANS: B

5. ANS: B

6. ANS: C

7. ANS: D

8. ANS: B

9. ANS: C

10. ANS: C

11. ANS: B

12. ANS: C

13. ANS: B

14. ANS: D

15. ANS: B

16. ANS: C

17. ANS: B

18. ANS: A

19. ANS: D

20. ANS: D

21. ANS: D

22. ANS: D

23. ANS: C

24. ANS: B

25. ANS: D

26. ANS: A

27. ANS: A

28. ANS: B

29. ANS: B

30. ANS: A

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