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Alg 2 BC -- Unit 6 Review

1. Look at the data in the chart below.

|x |0 |2 |4 |6 |8 |

|y |0.2 |2.1 |1.3 |0.9 |3.4 |

a) Use your calculator to find a cubic equation, f(x), that models the data.

b) Use your cubic equation (and the calculator) to calculate f(7).

2. [pic]

a) Write the polynomial in standard form.

b) Classify the polynomial according to its degree.

c) Use synthetic division to calculate [pic]

3. List all the possible rational zeros of each of the functions below. Then find all the zeros and graph using intercepts and end behavior

a) [pic]

b) [pic]

c) [pic]

4. a) Solve for x. Write your answer in interval notation

[pic]

b) Graph the inequality [pic]

5. A polynomial with integer coefficients has a degree of 3. Is it possible for the polynomial to have:

a) 2 imaginary roots? Explain.

b) 3 imaginary roots? Explain.

c) 4 imaginary roots? Explain.

6. Find the 5th term of the binomial expansion: [pic]

7. Expand [pic]

8. Write the equation of a polynomial that has integer coefficients and zeros of x = 2 and x = 3 – i.

9. Use long division to solve [pic]

10. An open box with a square bottom is to be made out of 150 square feet of material. What is the maximum volume of this box?

Extra Binomial Theorem Problems:

1. Find the third term of [pic]

2. Find the eighth term of [pic]

3. Find the coefficient of the term with [pic] in the expansion of [pic]

4. Find the coefficient of the term with [pic]in the expansion of [pic]

Answers!

1. a) [pic]

b) [pic]

2. a) [pic]

b) quartic

c) 240

3. a) b)

zeros: zeros:

. x = -1, 1, 3 x = -2, -1/2, 2/3

c) zeros: x = -1/2, [pic]

4. a) [pic] b)

5. a) yes. Imaginary roots come in pairs

b) no. imaginary roots must come in pairs.

c) no. there are only 3 total complex roots for a poly of degree 3.

6. [pic]

7. [pic]

8. [pic]

9. [pic]

10. 176.78 ft3

Answers to extra problems: 1. 84x5y2 2. 3240x6y14 3. 240 4. -108

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