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1. |
State the degree of the polynomial function f(x) = x4 - 2x2 + 3x - 1. |
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A. |
2 |
B. |
5 |
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C. |
4 |
D. |
3 |
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Hint |
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2. |
Write a polynomial equation of least degree with roots -1, 2i, and -2i. |
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A. |
3x + x2 + 4x - 4 = 0 |
B. |
x3 + x2 + 4x + 4 = 0 |
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C. |
x3 + x2 - 4x + 4 = 0 |
D. |
x3 - x2 + 4x + 4 = 0 |
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Hint |
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3. |
The roots of the equation x2 - 8x - 20 = 0 are ____. |
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A. |
-2 and -10 |
B. |
2 and 10 |
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C. |
-2 and 10 |
D. |
2 and -10 |
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Hint |
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4. |
Find the discriminant of x2 - 2x + 20 = 0. |
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A. |
76 |
B. |
-72 |
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C. |
-76 |
D. |
72 |
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Hint |
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5. |
If you divide a polynomial by the factor x + 6 and a remainder of zero results, which conclusion is true? |
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A. |
x + 6 is not a factor of the polynomial. |
B. |
x - 6 is not a factor of the polynomial. |
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C. |
x - 6 is a factor of the polynomial. |
D. |
x + 6 is a factor of the polynomial. |
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Hint |
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6. |
Determine the binomial factors of x3 - 5x2 - x + 5 = 0. |
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A. |
x - 1, x + 1, and x - 3 |
B. |
x + 1, x - 1, and x - 4 |
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C. |
x + 1, x - 1, and x - 6 |
D. |
x - 1, x + 1, and x - 5 |
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Hint |
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7. |
List the possible rational roots of 3x3 + 5x2 - 2x + 1 = 0. |
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A. |
1,  |
B. |
,  |
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C. |
1,  |
D. |
,  |
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Hint |
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8. |
In a polynomial equation, if there is one change in sign of the coefficients of the terms, ____. |
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A. |
there could be one or three positive real zeros |
B. |
none of the above is correct |
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C. |
there is one imaginary root |
D. |
there is exactly one positive real zero |
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Hint |
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9. |
Determine between which consecutive integers the real zeros of f(x) = x4 - 4x2 + x - 3 are located. |
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A. |
between -2 and -1 and between 2 and 3 |
B. |
between -4 and -3 and between 3 and 4 |
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C. |
between -3 and -2 and between 5 and 6 |
D. |
between -3 and -2 and between 2 and 3 |
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Hint |
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10. |
Determine the number of complex zeros of the function f(x) = x5 - 4x2 + 2x - 1. |
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A. |
3 |
B. |
4 |
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C. |
2 |
D. |
5 |
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Hint |
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11. |
Solve = 3. |
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A. |
-1 |
B. |
2 |
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C. |
3 |
D. |
2, 3 |
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Hint |
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12. |
Solve > 0. |
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A. |
-2 < x < 0 or x < 1 |
B. |
-1 < x < 0 or x > 1 |
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C. |
-1 < x < 0 or x > 2 |
D. |
-2 < x < 0 or x > 2 |
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Hint |
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13. |
Solve . |
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A. |
0 |
B. |
2 |
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C. |
3 |
D. |
1 |
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Hint |
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14. |
Solve 4. |
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A. |
x 0 |
B. |
0 x 8 |
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C. |
x 8 |
D. |
none of these |
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Hint |
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15. |
Determine the type of polynomial function that could be used to represent the data in the following scatter plot. |
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A. |
quartic |
B. |
linear |
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C. |
cubic |
D. |
quadratic |
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Hint |
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16. |
Use a graphing calculator to write a polynomial function to model the set of data. |
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A. |
1.3x - 0.9 |
B. |
0.9x + 1.3 |
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C. |
0.9x - 1.3 |
D. |
1.3x + 0.9 |
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Hint |
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