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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. |
3 |
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C. |
5 |
D. |
4 |
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Hint |
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2. |
Determine the zeros of the function y = x3 + 2x2 - 5x - 6. |
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A. |
-3, 2, 0 |
B. |
-1, 2, 3 |
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C. |
-3, -1, 2 |
D. |
-3, -1, 4 |
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Hint |
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3. |
Solve the equation 2x2 -x + 4 = 0 by any method. |
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A. |
 i |
B. |
i |
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C. |
1  i |
D. |
 i |
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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. |
76 |
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C. |
-72 |
D. |
72 |
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Hint |
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5. |
Divide x4 + 2x2 - 1 by x - 1 using synthetic division. The result of synthetic division is ____. |
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A. |
1 3 1 3 | -2 |
B. |
1 3 1 3 | 2 |
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C. |
1 1 3 3 | 2 |
D. |
1 1 3 3 | -2 |
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Hint |
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6. |
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 a factor of the polynomial. |
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C. |
x + 6 is not a factor of the polynomial. |
D. |
x + 6 is a factor of the polynomial. |
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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 is exactly one positive real zero |
B. |
there is one imaginary root |
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C. |
there could be one or three positive real zeros |
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 -3 and -2 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 -2 and -1 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. |
2 |
B. |
4 |
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C. |
3 |
D. |
5 |
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Hint |
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11. |
Decompose  into partial fractions. |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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12. |
Solve  > 0. |
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A. |
-1 < x < 0 or x > 1 |
B. |
-2 < x < 0 or x < 1 |
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C. |
-2 < x < 0 or x > 2 |
D. |
-1 < x < 0 or x > 2 |
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Hint |
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13. |
Solve  . |
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A. |
5, 2 |
B. |
2 |
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C. |
5 |
D. |
5, 1 |
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Hint |
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14. |
Solve the equation  = y. |
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A. |
3 |
B. |
None is correct. |
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C. |
-3 |
D. |
3, 9 |
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Hint |
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15. |
How many direction changes are there in the graph of a linear equation? |
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A. |
0 |
B. |
3 |
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C. |
2 |
D. |
1 |
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Hint |
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16. |
Use the function of best fit, y = 0.9x + 1.3, to predict y when x = 5. |
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A. |
2.3 |
B. |
3.2 |
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C. |
5.8 |
D. |
6.7 |
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Hint |
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