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Review #1: Algebra Review
Factor.
1. 4x2 – 25
3. x3 – x2 – 4x + 4
2. 8x3 + 27
4. 6x3 – 17x2 + 10x
5. x4 + 5x2 - 36
Simplify.
6.
8.
x3  1
x 2  5x  6
3
x2  x  2
1
10.
y2
2
x
y
1
x


x 2  3x  2
x 2  4x  4
5
x2  x  6
3x 4  10x 2  8 3x  6
7.

x2
15x 2  10
9.
3
8

2x  10 3 x  15
3
2

11. x  1 x  1
2
2

x 1 x
Solve.
12. 3x2 – 7x = -2
13. x2 – 5x = 0
14. 16x2 – 40 = 0
15.
3x
4x
84


2
x  4 x  3 x  x  12
16. 3x  7  5
17.
3
18
x


2
3 x x 9 3x
18. x  1 x  5
19. P =
ab
ab
for b
20. V =
1 2
 r h for h
3
Solve each problem involving linear functions. Write equations in
slope-intercept form.
21. Write the equation of a line through the points (-4, 7) and (-6, 2).
22. Write the equation of a vertical line through the intersection of the lines
3x + 4y = 2 and 2x + 5y = -1.
23. Find the equation of the perpendicular bisector of line segment AB where
A(-5, 8) and B(-1, -2).
24. Find the length of AB .
Answers to Review #1
1.
2.
3.
4.
5.
(2x – 5)(2x + 5)
(2x + 3)(4x2 – 6x + 9)
(x – 1)(x + 2)(x – 2)
x(x – 2)(6x – 5)
(x + 2)(x – 2)(x2 + 9)
x2  x  1
x 3
3( x  2)2
7.
5
2
8.
( x  1)( x  3)
25
9.
6(x  5)
xy
10.
x
x 5 x  1
11.
2x  1
1
12. 2,
3
13. 0, 5
10
14. 
2
15. No Solution (-4 and 3 were
extraneous)
2
16. 4,
3
17, -9 (3 was extraneous)
18. -3 (-8 was extraneous)
Pa
19. b 
a P
3V
20. h 
 r2
5
21. y = x + 17
2
22. x = 2
2
21
23. y  x 
5
5
24. 2 29
6.
Answers to Review #1
1.
2.
3.
4.
5.
(2x – 5)(2x + 5)
(2x + 3)(4x2 – 6x + 9)
(x – 1)(x + 2)(x – 2)
x(x – 2)(6x – 5)
(x + 2)(x – 2)(x2 + 9)
x2  x  1
x 3
3( x  2)2
7.
5
2
8.
( x  1)( x  3)
25
9.
6(x  5)
xy
10.
x
x 5 x  1
11.
2x  1
1
12. 2,
3
13. 0, 5
10
14. 
2
15. No Solution (-4 and 3 were
extraneous)
2
16. 4,
3
17, -9 (3 was extraneous)
18. -3 (-8 was extraneous)
Pa
19. b 
a P
3V
20. h 
 r2
5
21. y = x + 17
2
22. x = 2
2
21
23. y  x 
5
5
24. 2 29
6.