Opener – Remember your factoring???
Factor each expression. (take out common monomial, unfoil, or special factors difference of squares,
sum or difference of cubes)
1. x 2  3x  4
2. 4 x 2  9
3. 6x 2  x
4. 8 x 3  1
8.4 Rational Expressions
a c ac
 
b d bd
ka a

kb b
a  x  k  a  x 
b  x k b  x 
 a  x  b  x   b  x
 a  x  c  x  c  x
Example 1
x 2  4 x  12
Simplify
x2  4
12  4 x
x2  9
Example 2
5x 2 y 6 x 3 y 2
Multiply

2 xy 3 10y
x 2  7x  10
x 2  3x  10
x 2  5x  6
x2  1
Try
6 x 2 y 3 10 x 3 y 4

2 x 2 y 2 18y 2
Example 3
Multiply
4 x  4 x2 x2  x  6

x 2  2x  3
4x
Try
3x  27x 3 3x 2  4 x  1

3x 2  2 x  1
3x
Example 4
x 3
  4 x 2  2 x  1
8x3  1
Try
x 2
 9x2  6x  4 
27x 3  8
Dividing Rational Expressions
a c a d ad
   
b d b c bc
Example 1
5x
x 2  2x

3x  12 x 2  6 x  8
Example 2
6 x 2  7x  3
  2 x 2  3x 
6x2
3
x 2  3x
Try

4 x  8 x2  x  6
Try
8 x 2  10 x  3
  4 x2  x 
4 x2
Try
x
4 x2  9
  2 x  3 
x 2
x 2
Example 3
Simplify
x
9 x 2  25
  3x  5  
x5
x5
Example 4
2x 2  x  15
2x  5
6x  9 
2
2x  11x  21
3x  21
p.531 8-24 even, 27-29, 32-35, 42