Expert: Richard J. Raridon - 6/13/2009

Question
18. Solve:
(x^2 - 1)(x^2 + 3x + 2) = 0

19. Solve:
x^2(x^4 + 16) = 8x^4  

20. Solve: (Hint: Multiply the equation by a number to eliminate the decimals or fractions)
0.2x^2 - 1.1x + 0.5 = 0


21. Solve:
(t - 2)3 - (t - 2) = 0

22. Solve:
(x^2 - 3)2 + (x^2 - 3) - 2 = 0

23. Find all of the zeros for f:
f(s) = 4s^4 - 17s^2 + 4

24. Find two consecutive odd integers such that the sum of their squares is 130.  

25. The side of a large tent is in the shape of an isosceles triangle whose area is 54 ft² and whose base is 6 feet shorter than twice its height.  Find the height and the base of the tent (height by base).

26. A farmer plans to use 21 m of fencing to enclose a rectangular pen having an area of 55 m².  Only three sides of the pen need fencing because of an existing wall.  Find the dimensions of the pen.  

27. A decorator plans to place a rug in a room 9 m by 12 m in such a way that a uniform strip of flooring around the rug will remain uncovered.  If the rug is to cover half the floor space, what should the dimensions of the rug be?

28. Solve the inequality:
x^2 ≤ 9

29. Solve the inequality:
3s^2 < 48


30. Solve the inequality:
r^2 ≤ 2(r + 4)

31. Solve the inequality:
t^3 < 9t^2


32. Solve the inequality:
4x(x + 1) ≥ 3


33. Factor the following polynomial:
250x^2 - 2x^5


34. Factor the following polynomial:

p^4 - q^4


35. Find all the zero's of f:
f(t) = (t - 3)2 - (t + 3)  

Answer
18. x = 1,-1,-1,-2
19. x = 0, 2,-2
20. x = 1/2, 5
21. if you really mean (t-2)*3-(t-2), then t = 2
if you mean (t-2)^3 -(t-2), then t = 1,2
22. x = 1,-1,2,-2
23. s = 1/2, -1/2, 2, -2
24. 7 and 9
25. h=9,b=12
26. the sides are 5,11,5 or 5.5,10,5.5
27. 9 by 6
28. -3 =< x =< 3
29. -4 < s < 4
30. -2 =< r =< 4
31. t < 9
32. x => 1/2 or x +< -3/2
33. 2x^2(5-x)(25+5x+x^2)
34. (p+q)(p-q)(p^2+q^2)
35. if you really mean (t-3)*2 -(t+3) then t = 9
if you mean (t-3)^2 -(t+3) then t = 3,4