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1. |
Determine the zeros of the function y = x3 + 2x2 - 5x - 6. |
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A. |
-3, 2, 0 |
B. |
-3, -1, 2 |
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C. |
-1, 2, 3 |
D. |
-3, -1, 4 |
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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. |
x3 + x2 + 4x + 4 = 0 |
B. |
x3 - x2 + 4x + 4 = 0 |
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C. |
x3 + x2 - 4x + 4 = 0 |
D. |
3x + x2 + 4x - 4 = 0 |
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Hint |
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3. |
If you solve 2m2 + 8m + 1 = 0 by completing the square, first divide each side of the equation by ____. |
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A. |
2 |
B. |
1 |
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C. |
8 |
D. |
 |
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Hint |
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4. |
Solve the equation 2x2 -x + 4 = 0 by any method. |
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A. |
1  i |
B. |
 i |
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C. |
 i |
D. |
i |
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Hint |
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5. |
Find the value of k so that the remainder of (x3 - 3x2 + kx - 6) ÷ (x + 2) is 0. |
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A. |
k = 6 |
B. |
k = -11 |
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C. |
k = 11 |
D. |
k = -13 |
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Hint |
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6. |
Use the Remainder Theorem to find the remainder for the division of
(x4 - 3x2 + 2x - 1) ÷ (x - 1). The remainder is ____. |
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A. |
2 |
B. |
1 |
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C. |
-1 |
D. |
0 |
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Hint |
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7. |
Find the number of positive real zeros for
f(x) = 3x5 + 2x3 + x2 + 7x - 1 = 0. |
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A. |
4 or 2 or 0 positive real zeros |
B. |
no positive real zeros |
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C. |
exactly 1 positive real zero |
D. |
4 or 2 positive real zeros |
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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. |
there is one imaginary root |
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C. |
there is exactly one positive real zero |
D. |
none of the above is correct |
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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 -3 and -2 and between 5 and 6 |
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C. |
between -4 and -3 and between 3 and 4 |
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. |
2 |
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C. |
5 |
D. |
4 |
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Hint |
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11. |
Solve  > 0. |
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A. |
-2 < x < 0 or x < 1 |
B. |
-1 < x < 0 or x > 2 |
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C. |
-1 < x < 0 or x > 1 |
D. |
-2 < x < 0 or x > 2 |
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Hint |
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12. |
Solve  +  <  . |
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A. |
a < 0 or a > 5 |
B. |
a < 0 or 0 < a < 5 |
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C. |
a > 0 or 0 < a < 5 |
D. |
0 < a < 5 |
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Hint |
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13. |
Solve  . |
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A. |
1 |
B. |
3 |
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C. |
2 |
D. |
0 |
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Hint |
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14. |
Solve   4. |
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A. |
0 x 8 |
B. |
x  8 |
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C. |
none of these |
D. |
x 0 |
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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. |
quadratic |
D. |
cubic |
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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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