Name ______________________
Advanced Algebra 1
Semester 2 Review
Factor completely. If the polynomial cannot be factored, write PRIME.
1. 6p3 – 2p3r2 + 8p2r3st
2. 32a2b – 8b
3. k2- k- 42
4. 6y2 + 13y – 5
5. z2 +z - 3
6. 4a2 – a – 5
7. 4 x 2 − 25
8. x 3 + 27
9. x 2 − 10x + 25
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Solve by factoring.
10. b2 – 3b + 2 = 0
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11. 4a2 – a – 5 = 0
Simplify.
a 2b 2
2
2
13. a b - b a
2x 2 -5x -12
2
14. 12x - 3x
12. 16x2 – 8x = -1
15.
x 2 + 5x + 4 1+ 2x
•
2x 2 + 3x + 1 x 2 −16
16.
a2 − b2 a + b
÷ 2
(cd) 3
c d
18.
1
x
+ 2
4 x − 8 x − 3x + 2
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17.
3
a +1
− 2
a + 6a + 9 a − 9
2
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Find the LCD.
12 10
, 2
2
19. x xy
2
5
,
20. 3a - b 6a - 2b
State the restrictions for the following.
3m + 9
21. m + 3
23.
Solve for h:
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1
A = bh
2
x+6
2
22. 36 - x
Divide using long division.
a 2 - 3a + 7
a-2
24.
Solve.
25.
3x 5x
=
10
6
26.
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4a + 1 3a − 4
=
7
3
27.
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3y + 5 3y + 2 3
−
=
2
5
10
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Simplify.
4
35
•
5
4
28.
29. 4 2 +
30.
72
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31.
6 18
18 6
32.
(
)
5+3
2
33.
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34. State the conjugate of 4 +
35.
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7.
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Solve.
36.
3x + 2 = 4
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5x + 1 − 6 = 8
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37. 2x2 – 128 = 0
121a 4 b10
38. (a – 25)2 = 9
1
5−2 3
Find the third side of the right triangle.
39. a = 3, b = 4, c = ____
40. a = 5, b = ____, c = 13
Solve by using the quadratic formula.
41. 5z2 + 11z + 2 = 0
42. 10y2 – y = 3
Find the discriminant and state the number of real roots.
43. 9y2 – 12y + 4 = 0
How does each of the parabolas open?
44. 6x2 – 4x + 9 = y
45. y = 8 – 5x2
Find the vertex of the given equations.
46. y = 5x2 – 3
47. y = x2 + 10x + 25
State the domain and range of the quadratic equation.
48. y = 2x2 - 6x - 8