1. factor completely 2x^4-12x^3+12x^2
2x2(x2 – 6x + 6)
2a. solve 2x^2=6
b. find x intercepts of f(x)=2x^2-6
type exact answers, use radicals as needed, rationalize all denominators
Solutions:
x-intercepts:
3, − 3
(
) (
3, 0 , − 3, 0
)
5. use foil to find product
(6x^5-7)(x^6-1)
6x11 – 7x6 – 6x5 + 7
11. state value of discriminant
18x62+10x-20=0
is there one real solution or 2 imaginary solutions or 2 real solutions?
Discriminant = 1540
Equation has 2 real solutions
13. multiply (3x+5)(2x^2+4x+7)
6x3 + 22x2 + 41x + 35
14. simplify 12 over radical (-3)^12
12
12
(−3)
=3
16. multiply (-4x)^2(3x^5)^2
144x12
18. solve 5/z = 7/z-1/5
z = 10
19. find vertex, line of symmetry, the maximum OR minimum value for x, state whether
is it max or min and if graph opens up or down
f(x)=1/3(x+2)^2+6
Vertex is (-2, 6)
Line of symmetry is x = -2
Minimum value of f(x) is 6
f(-2) = 6 is a minimum
Graph opens up
Graph looks like this:
22. 81a^2-121 factor binomial
(9a + 11)(9a – 11)
26. use rational exponents to write x^1/2 times y^1/6 times z^1/3 as single radical
expression
6
x 3 yz 2
29. subtract simplify by collecting radical terms if possible 4 radical 32 ñ 4 radical 2
4 32 − 4 2 = 12 2
32. factor completely 100a^2+160af+64f^2
4(5a + 4f)2
33. evaluate polynomial for x= -3
3x^2-2x+7
40
34. divide and simplify
7x-56/121 divided by x-8/55x
7x − 56 x − 8 35x
÷
=
121
55x
11
35. perform operations and simplify
y-7/y-9 - y+1/y+9 + y-45/y^2-81
y − 7 y +1 y − 45
11
−
+ 2
=
y − 9 y + 9 y − 81 y + 9
38. use quadratic formula. type exact answers with radicals as needed
x^2-3x= -4
3+ i 7 3− i 7
, 2
2
39. find vertex, line of symmetry, max or min value for x and sate whether it is min or
max and if graph opens up or down
f(x)= -2x^2+2x+3
Vertex is (1/2, 7/2)
x-coordinate of the vertex is ½
y-coordinate of the vertex is 7/2
Line of symmetry is x = ½
Maximum value of f(x) is 7/2
f(1/2) = 7/2 is a maximum
The graph opens down.
The graph looks like this:
42. solve 4x^4-12x^2+5=0
x = ½, 5/2
43. solve (x+8)(x-14)(x+5) is greater than 0
-8 < x < -5, x > 14
46. in right triangle find length of side not given b=2, c= radical 13 a=????
a=3
47. type exact answer using radicals as needed x^2+6x-4=0
−3+ 13, −3− 13
48. (5 radical 5 - 15 radical 3)(2 radical 5 + 6 radical 3)
(5
)(
)
5 −15 3 2 5 + 6 3 = −220
52. find x intercepts of graph y = x^2 -2x - 8
(-2, 0), (4, 0)
57. solve b^2-4b-45=0
9, -5
60. factor 63-16r+r^2
(9 – r)(7 – r)
61. using V=48T^2 how many seconds will player hang if he has vertical leap of 25
inches? type decimal and round to nearest tenth
0.7
62. 4x(x-7)-5x(x-6)= -3 solve for x
-1, 3
64. multiply, simplify by factoring 3 over radical y^7 times 3 over radical 81y^8
3
y 7 3 81y8 = 3y 5 3 3
66. simplify 3 over radical -1/64
3
−
1
1
=−
64
4