4A
CHAPTER 4 TEST
Name:
1. Simplify. Write the polynomial in simplest form. Assume that variable exponents
a−b 2 a
2b 2
denote positive integers. (x ) (x + x )
3
2. _________________
4 m
m
1. _________________
2. Solve 81 (27) = (9 ) for m.
3−4. Express as a polynomial in simplest form. Assume that variable exponents denote
positive integers.
2
3. a b(6a − b)(a + 2b)
3. _________________
4. _________________
4. (m + 2n + 1)(3m − n − 1)
5. _________________
8 4 9
4
3
5−6. Find the GCF and LCM of 48x y z and 72x yz .
6. _________________
7−12. Factor completely.
4
3
7. 8x − 10x + 3x
7. _________________
2
8. 6xy − 9x + 10y − 15
2
2
9. 4x − y + 4y − 4
6
8. _________________
9. _________________
3
10. x + 64y
10. _________________
2
11. 3(a + b) − 11(a + b) − 4
12. 2x
3n
11. _________________
3m
− 2y
12. _________________
13. 2x
2n + 1
− 17x
n+1
+ 8x
13. _________________
14−15. Solve. Identify all double roots.
3
14. n = 16n
14. _________________
2
15. 24x = 26x − 6
15. _________________
16−17. Find all zeros of f. Identify all multiple zeros.
3
2
16. _________________
16. f(x) = 2x − 16x + 32x
3
17. f(x) = (4x − 3) − 25(4x − 3)
40
17. _________________
4A
CHAPTER 4 TEST
Name:
18−20. Select a variable. Tell what the variable represents. Write an equation.
Solve the equation. Write a sentence that answers the question.
18. _________________
18. When 1 cm was planed off each of the six faces of a wooden cube, its volume was
3
decreased by 296 cm . Find the new volume.
19. _________________
19. A rectangular corner lot originally had dimensions 90 m by 100 m, but one fifth of
its original area was lost when the two adjacent streets were widened by the same
amount. Find the new dimensions of the lot.
20. _________________
20. A ball is thrown upward from the top of a building 88.2 m high with an initial
upward speed of 14.7 m/s. After how many seconds will it strike the ground?
2
(Use h = k + vt − 4.9t )
21. _________________
21. Solve algebraically. Show all steps.
2
x < −2x + 15
22. _________________
22−24. Graph the solution set of each inequality.
2
22. −x − 2x < −8
−10 −8
3
−6
−4
−2
0
2
4
6
8
10
−4
−2
0
2
4
6
8
10
−4
−2
0
2
4
6
8
10
23. _________________
2
23. 2x − 2x − 12x > 0
−10 −8
4
−6
24. _________________
2
24. x − 10x + 9 < 0
−10 −8
−6
EC1. _________________
Extra Credit.
4
2
1. Factor completely: (x + 4) + (x − 2x + 2)
2
2. Write an algebraic equation and solve.
If the width of a box were increased by 1 cm, the height increased by 3 cm, and the
length decreased by 2 cm, the volume of the resulting cube would exceed the volume
3
of the original box by 127 cm . Find the dimensions of the original box.
41
EC2. _________________
4A
CHAPTER 4 TEST
Name:
Answers:
1. x
4a − 2b
3a
+ 2x + x
2a + 2b
2. m = 12/5
4
3 2
2 3
3. 6a b + 11a b - 2a b
2
2
4. 3m + 2m + 5mn - 3n - 2n - 1
4
3
5. 24x yz
8 4 9
6. 144x y z
2
7. x (4x - 3)(2x - 1)
8. (2y - 3)(3x + 5)
9. (2x - y + 2)(2x + y - 2)
2
4
2
2
10. (x + 4y)(x - 4x y + 16y )
11. (3a + 3b + 1)(a + b - 4)
n
m
12. 2(x - y )(x
2n
n
n m
2m
+xy +y )
n
13. x(2x - 1)(x - 8)
14. {-4, 0, 4}
15. {1/3, 3/4}
16. {0, 4 d.z}
17. {-1/2, 3/4, 2}
18. 216 cm
3
19. 80 m by 90 m
20. 6 sec
21. -5 < x < 3
22. x < -4 or x > 2
23. -2 < x < 0 or x > 3
24. -3 < x < -1 or 1 < x < 3
2
2
EC1. 2(x - 2x + 2)(x + 2)
EC1.
EC2. 6 by 4 by 9
x + 4x + 4 - 4x
2
2
2
(x + 2) - (2x)
2
2
(x + 2x + 2)(x - 2x + 2)
42
4
2
2