Math 131
Test 3
Show all necessary steps Clearly, Neatly, and Systematically to receive full credit.
Name:____________________
From # 1 - 6, do 5 problems. If you do more, the first 5 problems will be graded.
1.
a.
i.
Let f ( x)  2 x  5 , g ( x)  x 2  5 x  3 , and h( x)  x3  6 x 2  17 x  2 .
Find ( f  g  h)( x) .
ii. Find ( f  g  h)(1) .
b.
Solve: (3x  2)( x  4)  x( x  1)  (2 x  1)( x  4)  12
2.
a.
Multiply:
i.
2  3
2
3
 y   y  
3  2
3
2
b.
Perform indicated operation:
ii.
5  (a  b)5  (a  b)
iii.
(m  4)  h2
x 1
1
4x  1

 2
x  16 x  4 3 x  7 x  20
2
3.
a.
5m  5 m 2  2m  24 3m 2  17m  20
Perform indicated operation: 2


m  6m m 2  3m  4
5m 3  20m 2
b. Factor Completely.
8a 4b 2  12a 3b3  36ab 4
i.
ii. c 3  c 2  5c  5
iii. 24m 2  58mn  9n 2
iv. 18 x 2  37 x  20
4.
a.
 24 y 2 z  39 yz  18z
vi. 169r 2  289s 2
vii. 12 p 2  75q 2
v.
viii. 3( z  3)2  14( z  3)  8
ix.
16k 4  81
Perform long division: (2 x 4  7 x3  50 x 2  10 x  96)  ( x 2  x  3) .
6
b. Simplify: x  5 x  6
2
3

x3 x2
2
c.
Let f ( x)  x3  13x  17 . Use the Remainder Theorem to find f (3) .
d. Divide:
5. Solve:
x 4 y 4  8x 2 y 2  4 xy
4 x3 y
7
4y
6
 2
 2
y  y  12 y  7 y  12 y  9
2
6.
a. Solve: 2c 3  3c 2  8c  12
b. Simplify:
a 2 b 1  a 1b 2
4a 2  4b 2
From # 7 - 12, do only 5 problems. If you do more, the first 5 problems will be graded.
7. Solve:
5
3
 . Write the solution in interval notation and graph.
x2 x
8. Solve the inequality and write the solution in interval notation:  3m 2  16m  5 .
9. A river has a current of 4 km per hr. Find the rate of Herby's boat in still water if it goes 40 km down stream in the
same time that it takes to go 24 km up stream. (make sure to show in 3-steps format)
10. The width of a rectangle is twice its length. If its width is increased by 3 in., and its length is increased by 7 in., then
the area of the new rectangle is 40 in. 2 . Find the dimensions of the original rectangle. (make sure to show in 3-steps
format)
11. If a rock is dropped from a building of 576 ft high, then its distance in feet from the ground t second later is a
function defined by f (t )  16t 2  576 . How long after it is dropped will it hit the ground?
12. Alexandra and Frank can assemble a King Kong swing set working together in 6 hours. One day, when Frank called in
sick, Alexandra was able to assemble a King Kong swing set in 10 hours. How long would it take Frank to assemble a King
Kong swing set if he worked by himself? (make sure to show in 3-steps format)