Slide 1

2.4 – Factoring Polynomials
Tricky Trinomials

ax  bx  c
2


Slide 2

A tricky trinomial is a quadratic expression where
the leading coefficient is not a 1.

ax  bx  c
2

You should try to common factor first but
sometimes you can’t factor out the leading
coefficient! There are four methods for
factoring tricky trinomials:
 Decomposition
 Tabletop Method
 Australian Method
 Algebra Tiles


Slide 3

DECOMPOSITION

This method stinks!


Slide 4

Factor:

4  3  12
6 = -8
 2 + ___
___

4x  8x  3
2
 4 x  2 x  6 x  3 ___
2
2

Common Factor

Common Factor

 2 x(2 x  1)  3(2 x  1)
Common Factor

 (2 x  1)( 2 x  3)

6 = 12
x 
___

Factors of 12
1 x 12
2x6
3x4


Slide 5

Factor: 12  6  72

12 x  x  6
2

 8 + ___
9 = -1
___

 12 x  8 x  9 x  6 ___
8
2

Common Factor

Common Factor

 4 x(3 x  2) 3(3x  2)
Common Factor

 (3x  2)( 4 x  3)

9 = -72
x 
___

Factors of 72
1 x 72
2 x 36
3 x 24
4 x 18
6 x 12
8x9


Slide 6

AUSTRALIAN METHOD

Because of the one down under!


Slide 7

Factor:

4  3  12

4 x  8 x  3 ___
2
( 4 x  2 )( 4 x  6 )
=
2

Common Factor

one “down under”

Common Factor

4

= 2( 2 x  1)2( 2 x  3)
4

= ( 2 x  1)( 2 x  3)

6 = -8
+ 
___

2 x 
6 = 12
___
___

Factors of 12
1 x 12
2x6
3x4


Slide 8

Factor:

5  6  30

5 x  17 x  6 ___
2
( 5x  2 )( 5x  15 )
=
2

Common Factor

one “down under”

Common Factor

5

= 1(5 x  2) 5( x  3)
5

= (5 x  2) ( x  3)

+ 15
___ = 17

2 x 15
___
___ = 30

Factors of 30
1 x 30
2 x 15
3 x 10
5x6


Slide 9

Homework:
PAGE 109 #2, 4 – 14