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1. |
What is the leading coefficient of the polynomial
p(x) = -3x5 + 4x3 - 5x2 + 4x - 6? |
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A. |
4 |
B. |
-6 |
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C. |
-3 |
D. |
3 |
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Hint |
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2. |
When x3 - 4x2 + x - 5 is divided by x - 2, the quotient is _____. |
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A. |
x2 - x + 25 |
B. |
x - 2 |
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C. |
-11 |
D. |
x2 - 2x - 3 |
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Hint |
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3. |
Find f(x + h) for f(x) = x2 + 2x. |
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A. |
x2 + 2x + h |
B. |
x2 + 2xh + h2 + 2x + 2h |
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C. |
x2 + 2x + 2h |
D. |
x2 + 2xh + h2 + 2x |
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Hint |
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4. |
Approximate the real zero of f(x) = x3 + x + 1 to the nearest tenth. |
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A. |
0.3 |
B. |
-1.3 |
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C. |
-1.0 |
D. |
-0.7 |
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Hint |
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5. |
How many possible negative real zeros are there for the polynomial
g(x) = 2x4 + x3 - 4x + 1? |
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A. |
3 |
B. |
1 |
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C. |
2 |
D. |
5 |
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Hint |
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6. |
List all possible rational zeros of f(x) = 2x3 - 5x2 + 3x - 1. |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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7. |
Manufacturing A company sells one of its products in boxes that are twice as long as they are wide, and 2 inches higher than they are long. Find the dimensions of such a box if the volume is 320 cubic inches. |
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A. |
4 in. by 8 in. by 10 in. |
B. |
4 in. by 8 in. by 6 in. |
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C. |
4 in. by 8 in. by 20 in. |
D. |
6 in. by 12 in. by 14 in. |
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Hint |
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8. |
Solve x4 - 5x2 + 4 = 0. |
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A. |
-1, 1 |
B. |
-1, 1, -2, 2 |
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C. |
-1, 1, -2i, 2i |
D. |
1, 2 |
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Hint |
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9. |
Find g[h(x)] if g(x) = x2 and h(x) = x + 3. |
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A. |
x2 + x + 3 |
B. |
x2 - x - 3 |
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C. |
x2 + 6x + 9 |
D. |
x3 + 3x2 |
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Hint |
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10. |
Which pair of functions are inverses? |
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A. |
f(x) = 2x + 1,
g(x) = 2x - 1 |
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B. |
f(x) = 4x, g(x) = -4x |
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C. |
 |
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D. |
 |
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Hint |
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11. |
Graph  . Then estimate the coordinates at which the relative maxima and relative minima occur. |
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A. |
minimum: 1, maximum: –3 |
B. |
minimum: –3,maximum: 1 |
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C. |
minimum: 1,maximum: –5 |
D. |
minimum: –5,maximum: 1 |
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Hint |
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12. |
Write the expression  in quadratic form. |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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13. |
What must be true in order for a term x – a to be a factor of a polynomial f(x)? |
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A. |
a must be positive |
B. |
f(a) = 0 |
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C. |
f(a) must be negative |
D. |
f(a) must be positive |
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Hint |
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14. |
Find all of the roots of the equation  |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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15. |
Let f and g be polynomials of degree 3. Is it true that  ? |
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A. |
No, it is only true for polynomials of degree 1. |
B. |
It is true in some cases. |
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C. |
Yes, always. |
D. |
No, never. |
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Hint |
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16. |
Find the inverse of f(x) =  x – 3. |
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A. |
g(x) = x + 12 |
B. |
g(x) = 4x + 12 |
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C. |
g(x) = x + 3 |
D. |
g (x) = 4x + 3 |
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Hint |
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17. |
What is the domain and range of  ? |
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A. |
D: 
R:  |
B. |
D:
R:  |
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C. |
D: 
R: |
D. |
D:
R: |
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Hint |
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18. |
What are the x- and y-intercepts of  ? |
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A. |
x: , y: –5 |
B. |
x: –5, y: |
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C. |
x: no intercept, y: |
D. |
x: 5, y: |
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Hint |
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