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MATH 070
Sample Test 3A
1) Factor completely:
a)
b)
c)
d)
e)
f)
g)
14 x 3 y  7 x 2 y  7 xy
x3  x 2  4x  4
18 x 2  9 x  14
4 x 2  36 xy  81y 2
y 4  25
125  R 3
12 x 2  46 xy  8 y 2
2) Solve for y : 6 y 2  22 y  40
In problems 3, 4, and 5 you must identify any variables introduced, write and solve an
appropriate equation. In problem 4 you must draw and label a figure appropriately.
3) The sum of two numbers is 25, and the sum of their squares is 325. Find the
numbers.
4) Two boats travel at a right angle to each other after leaving the same dock at the same
time. One hour later the boats are 17 miles apart. If one boat travels 7 miles per hour
faster than the other boat, find the rate of each boat.
5) A 6-foot tall person drops an object from the top of the Western Peachtree Plaza in
Atlanta, Georgia. The Westin building is 723 feet tall. The height h of the object after t
seconds is given by the equation h  16t 2  729 . Find how many seconds pass before
the object reaches the ground.
1
x2  7x

6) Divide:
 x  4 x 2  3x  28
7) Simplify:
13
5

x  5x  6 x  3
2
Answers:
1) a)
b)
c)
d)
e)
f)
g)
2)
7 xy(2 x 2  x  1)
( x  1)( x 2  4)
(6 x  7)(3x  2)
(2 x  9 y ) 2
( y 2  5)( y 2  5)
(5  R)( 25  5R  R 2 )
2( x  4 y )(6 x  y )
4
,5
3
3) 10 and 15
4) Slow boat, 8 mph; fast boat, 15 mph
5) 6.75 sec.
6)
1
x
7)
 5 x  23
( x  3)( x  2)
MATH 070