Problem Set 3
Algebra Review for Pre-Calculus
Solve the word problems. Write your answers as complete sentences.
1. Mike and Kathleen ordered a large pizza that
2. Don ordered a jumbo pizza and ate ⅓ of it.
costs $10.00. Mike ate ⅝ of the pizza and
His friend Tom ate ¾ of what was left. How
Kathleen ate the rest. Based on consumption,
much of the original pizza did Tom eat? Who ate
how much should each one pay to share the cost
more, Don or Tom? How much pizza was left
fairly?
over?
Use factoring to reduce each rational expression to lowest terms.
3x 2
x3  x
3.
4. 3
9 x  18
x  x2
5.
x 2  4x  4
x 2  6x  8
x2  x  6
7.
9x  x3
9.
x3  x2  x
x3 1
6.
3y  2
3y  5y  2
2
x2  x  2
8.
2 x 2  3x  2
10.
4 x 2  12 x
3x 2  10 x  3
Find the values, if any, which must be excluded from the domain of the functions below.
2 x 2  3x  4
x2  9
x 2  4 x  12
11. f ( x) 
12. g ( x)  2
13. h( x) 
x5
x 9
x 2  36
Simplify the expressions below. Leave your answer in factored form.
x 2  7 x  6 x 2  5x  6
2x 2  x  3 4x 2  9
14.
15.


x 2  x  6 x 2  5x  6
2x 2  x  3 x 2  1
x2  4
2
16. 3x
x2
18 x
x 2  7 x  12
2
17. x 2  7 x  12
x  x  12
x 2  x  12
8x 2  6x  1
4x 2  1
18.
12 x 2  5 x  2
6x 2  x  2
3x 2  2 x  1
2
19. 5 x 2  9 x  2
2x  x  3
10 x 2  13 x  3