Math253
Practice Exam #02
1. Multiply the polynomials and simplify by combining like terms.
a)
( ab + c )( ab − c )
b)
( r + 3)( r + 2 )( r − 1)
2. Factor the following trinomials.
b) x 2 + 12 xy + 27 y 2
b) 9a 2 + 18a + 8
3.
Factor completely.
a) p 2 q 2 − 16
b) ( a + b ) − 25
2
4. Factor the following.
a) x3 − 27
b) a 3 + 18
5. Solve each equation.
a)
0
( 2t + 5)( t − 7 ) =
b) 9 x 2 − 15 x + 4 =
0
c) 4a 2 − 25 =
0
6. Subtract and simplify.
4xy
x− y
−
2
x −y
x+ y
2
7. Solve the equation.
3
4
x
+
=
2
x x + 2 x + 2x
8. Simplify each rational expression.
a)
a 2 − b2
ab
a −b
b
b)
1
3
+
x − 2 x −1
2
5
+
x −1 x + 2
9. A Hudson River tug boat goes 10 mph in still water. It travels 24 mi upstream and 24 miles
back downstream in a total time of 5 hours. What is the speed of the current?
10. The weight M of an object on mars varies directly as its weight E on earth. A person who
weighs 95 pounds on earth weighs 38 pounds on mars. How much would a 100 pound person
weigh on Mars?