1. Find a cubic equation that has zeros -2, 4, and 6 and passes through (1,5).
2. Find f(2) if f(x) = 2x3 - 3x2 + x - 1, using the Remainder Theorem.
3. Use the Factor Theorem to determine if x - 1 is a factor of f(x) = x4 - 2x2 + 1.
4. Graph y = (x - 2)(x + 1)2 (x - 1)3.
5. A rectangular enclosure, subdivided
into three congruent pens as shown, is to be
made using
a barn as one side and 120 m of fencing for the rest of the
enclosure.
Find the
value of x that gives the maximum area for the enclosure.
____________
|
| |
|______|______|
|
barn |
|____________
|
6. Find the area of the largest rectangle
(with sides parallel to the coordinate axes) that can be inscribed in the
region
enclosed
by the graphs of f(x) = 18 - x2 and g(x)
= 2x2 - 9.
7. Find the equation of the parabola whose x-intercepts are x = 3 and x = 11 and that passes through (1,-2).
8. Graph y = 2x2 + 4x - 1.
9. 7 + \/(-4) - 5\/(-1) - 7i +8 =
10. Simplify: 5 - 2i
3 + i
11. Plot -4 + i in the complex plane.
12. Write x4 - 2x2
- 3 as a product of
a.
linear factors over complex numbers
b.
two linear factors and one quadratic factor over real numbers
c.
two quadratic factors over rational numbers
13. Find a fourth degree polynomial function that has zeros: 3,1,2,5
14. Find all real and imaginary roots of the polynomial equation x4 + x3 + 2x2 - x - 3 = 0.
15. Find all zeros of the function f(x) = 2x3 - 4x2 + 5x - 3 = 0
16. Given that 5i is a zero of f(x) = 2x3 + 3x2 + 50x + 75, find the other zeros.
17. Look over these word problems: page 167/56,57; page 179/75; page 194/93,94