1. Identify the left-hand and right-hand behavior of the graph of the polynomial function f(x) = 6x3- 5x + 4.
2. Find a polynomial function that has zeros at -3, -1, and -2. Do not leave it in factored form, but multiply out your answer.
3. Use the Intermediate Value Theorem to determine an interval bounded by integers one unit in length in which the polynomial function is guaranteed to have a zero.
[EXPLAIN]
f(x) = 3x5- 9x4 + 5x3- 4x2 + x - 3
4. Use synthetic division to determine which of the following is a solution of the equation 3x4- 2x3 + 26x2- 18x - 9 = 0.
[A] 3 [B] 1 [C] - 3 [D] 1/3 [E] None of these
5. Use synthetic division to divide 4x4 - 4x3-8x - 14 by x - 2. Show your work and state the quotient and remainder.
6. Factor 2x3 + 15x2 + 27x +10 given that x+2 is one of the factors. SHOW YOUR WORK.
7. Determine the maximum number of zeros of the polynomial function
f(x) = 7x2 + 7x - 7x +2.
8. Use the Rational Zero Theorem to determine all possible rational zeros of
f(x) = 3x5 - 6x3 - 2x2 + 9
Do not find the actual zeros.
9. Find all the real zeros of the function f(x) = x3 + 2x2 - 13x + 10. SHOW YOUR WORK.
10. A polynomial function of degree 5 whose coefficients are real numbers has the zeros 2, -9i, and -9+i. Identify the remaining zeros.
11. Write this polynomial in completely factored form: 10x3 +29x2 + 4x - 15. SHOW YOUR WORK.
12. Use the Remainder Theorem, not direct substitution, to find f(-2) when
f(x) = 4x3 + 3x + 10. Show your work and specify what f(-2) is.
13. Wouldn't it be nice to win a million dollars? Most people think so, but one thing many forget to consider is the amount of taxes that must be paid on the winnings. The table below shows the relationship between the winnings and the approximate amount of taxes to be paid to the IRS. Draw a scatter plot to model the data. Then find an equation for the best-fit line and use the equation to estimate the amount of taxes tobe paid on winnings of $5,300,000.
| Amount Won |
Taxes Due |
| $470,000 |
$100,000 |
| $670,000 |
$180,000 |
| $1,420,000 |
$480,000 |
| $1,995,000 |
$710,000 |
| 2,545,000 |
$930,000 |