Ch 5

1
Ch 5

• Section 3 Factoring Trinomials of the Type ax2
  bx c

2
Introduction

• In section 2 we factored trinomials that looked
  similar to this
• In this section well do ones like this

x2 - 6x 7
1
3x2 4x - 15
3
3
FOIL Reviewed
First
Inner
Last
Outer

• (2x 5)(3x 4)

6x2
8x
15x
20
6x2 23x 20
4
FOIL Reviewed
First
Inner
Last
Outer

• (2x 5)(3x 4)

6x2
8x
15x
20
6x2 23x 20
2x(3x)
5
FOIL Reviewed
First
Inner
Last
Outer

• (2x 5)(3x 4)

6x2
8x
15x
20
5(3x)
6x2 23x 20
2x(4)
8x 15x
6
FOIL Reviewed
First
Inner
Last
Outer

• (2x 5)(3x 4)

6x2
8x
15x
20
6x2 23x 20
5(4)
7
Factoring 1 of 4
3x x
( )( )

• Factor

3x2 - 10x - 8
3x2
-10x
- 8
(-8)?1 8?(-1) (-2)?4 2?(-4)
1?(-8) (-1)? 8 4?(-2) (-4)?2
(3x 8)(x 1)
3x2 3x 8x 8
3x2 5x 8
8
3x2
Factoring 1 of 4
3x x
( )( )

• Factor

- 8
3x2 - 10x - 8
(-8)?1 8?(-1) (-2)?4 2?(-4)
1?(-8) (-1)? 8 4?(-2) (-4)?2
-10x
(3x 8)(x 1)
3x2 3x 8x 8
3x2 5x 8
9
3x2
Factoring 1 of 4
3x x
( )( )

• Factor

- 8
3x2 - 10x - 8
(-8)?1 8?(-1) (-2)?4 2?(-4)
1?(-8) (-1)? 8 4?(-2) (-4)?2
-10x
(3x 2)(x 4)
3x2 12x 2x 8
3x2 10x 8
10
3x2
Factoring 1 of 4
3x x
( )( )

• Factor

- 8
3x2 - 10x - 8
(-8)?1 8?(-1) (-2)?4 2?(-4)
1?(-8) (-1)? 8 4?(-2) (-4)?2
-10x
(3x 2)(x 4)
3x2 12x 2x 8
3x2 10x 8
11
Factoring 2 of 4
( )( )
( )( )
10x x
5x 2x

• Factor

10x2 37x 7
10x2
7
37x
1?7 -1?(-7)
7?1 -7?(-1)
(10x 1)(x 7)
10x2 70x 1x 7
10x2 71x 7
12
10x2
Factoring 2 of 4
( )( )
( )( )
10x x
5x 2x

• Factor

7
10x2 37x 7
1?7 -1?(-7)
7?1 -7?(-1)
37x
(10x 7)(x 1)
10x2 10x 7x 7
10x2 17x 7
13
10x2
Factoring 2 of 4
( )( )
( )( )
5x 2x
10x x

• Factor

7
10x2 37x 7
1?7 -1?(-7)
7?1 -7?(-1)
37x
(5x 1)(2x 7)
10x2 35x 2x 7
10x2 37x 7
14
First Term
Factoring Practice
(3x )(3x )
or
18x2 24x 10
(9x )(x )
2(9x2 12x 5)
Last Term
Middle Term
1?(-5) -1?5 (-5)?1 5?(-1)
(3x 1)(3x - 5)
-15x 3x
-12x
15
First Term
Factoring Practice
(3x )(3x )
or
18x2 24x 10
(9x )(x )
2(9x2 12x 5)
2
Last Term
Middle Term
1?(-5) -1?5 (-5)?1 5?(-1)
(3x - 1)(3x 5)
15x - 3x
Answer
12x
(3x - 1)(3x 5)
16
First Term
Factoring 3 of 4
(6x )(x )
or
24x3 76x2 40x
(3x )(2x )
4x(6x2 19x 10)
Last Term 10
Middle Term -19x
2?5 -2?(-5) 5?2 (-5)?(-2)
10?1 (-10)?(-1) 1?10 -1?(-10)
-19x
Answer 4x(3x - 2)(2x - 5)
17
First Term
Factoring 4 of 4
(3x )(x )
Rearrange Descending Order
10x 8 3x2
Last Term
3x2 10x 8

1(3x2 10x 8)
Middle Term
Answer -1(3x 2)(x - 4)
18
Practice

• MathXL Ch 5 Section 3 Homework

19
Chapter 5

• Section 4 Factoring Perfect-Square Trinomials
  and Differences of Squares

20
Review Perfect Square Trinomials

• From Chapter 4 Section 5

Perfect Square Trinomials
21
Perfect Square Trinomials 1 of 4
?
?
?
Is this a perfect square trinomial?
Yes!
22
Perfect Square Trinomials 1 of 4
Factor the perfect square trinomial
23
Perfect Square Trinomials 2 of 4
?
?
?
Is this a perfect square trinomial?
Yes!
24
Perfect Square Trinomials 2 of 4
Factor the perfect square trinomial
25
Perfect Square Trinomials 3 of 4
X
?
Is this a perfect square trinomial?
No
26
Perfect Square Trinomials 4 of 4
?
?
?
Yes!
Is this a perfect square trinomial?
27
Perfect Square Trinomials 4 of 4
Factor the perfect square trinomial
28
Review Difference of Squares

• From Chapter 4 Section 5

Difference of Squares
29
Difference of Squares
?
?
?
Is this a difference of squares?
Yes!
30
Difference of Squares
Factor the difference of squares
31
Difference of Squares
?
?
?
Is this a difference of squares?
Yes!
32
Difference of Squares
Factor the difference of squares
33
Difference of Squares
?
?
?
Is this a difference of squares?
Yes!
34
Difference of Squares
Factor the difference of squares
35
Difference of Squares
?
?
?
Is this a difference of squares?
Yes!
Factor out 2x2
36
Difference of Squares
Factor the difference of squares
37
Note
38
Factoring Completely
Difference of Squares A2 B2 (AB)(A-B)

• Factor

39
Practice

• MathXL Ch 5 Section 4 Homework