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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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