This document discusses factoring trinomials by grouping. It provides examples of factoring trinomials where the coefficient of the second term is not 1, such as 3x^2 + 14x + 8 = (3x + 2)(x + 4). The document shows how to determine the sum and product of the terms, then find two numbers with that sum and product to group the terms. It provides step-by-step workings for factoring trinomials like 10n^2 + 3n - 1 and 20g^2 - g - 1 using this method. The last example factors the trinomial 12x^5 + 10x^4 - 12x^3 in two steps.

1. Slide - 1Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
2
Factoring and
Applications
13

2. Slide - 2Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
1. Factor trinomials by grouping when the
coefficient of the second-degree term is not 1.
Objectives
13.3 Factoring Trinomials by Grouping

3. Slide - 3Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials by Grouping
Factor the trinomial 3x2 + 14x + 8.
Sum is 14.
Product is 24.
1 24
2 12
3 8
4 6
Find a product
of 24 and a
sum of 14.
3x + x + x + 82 2 12
x (3x + 2) + 4 (3x + 2)
(3x + 2) (x + 4)
(3x + 2) (x + 4) =Check: 3x2 + 14x + 8
Example
2
3 14 8x x 

4. Slide - 4Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials by Grouping
Factor the trinomial 10n2 + 3n – 1.
10n2 + 3n – 1
Sum is 3.
Product is – 10.
1 –10
2 –5
Find a product
of –10 and a
sum of 3.
10n2 + n – n – 15 2
5n (2n + 1) – 1 (2n + 1)
(2n + 1) (5n – 1)
(2n + 1) (5n – 1) =Check: 10n2 + 3n – 1
–1 10
–2 5
Example

5. Slide - 5Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials by Grouping
Factor the trinomial 20g2 – g – 1.
Sum is –1.
Product is – 20.
1 –20
2 –10
4 –5
Find a product
of –20 and a
sum of –1.
20g2 + g – g – 14 5
4g (5g + 1) – 1 (5g + 1)
(5g + 1) ( 4g – 1)
20g2 – g – 1
Check: (5g + 1) (4g – 1) = 20g2 – g – 1
Example

6. Slide - 6Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials by Grouping
–1 36
–2 18
–3 12
Find a product
of – 36 and a
sum of 5.
Factor 12x5 + 10x4 – 12x3
.
12x5 + 10x4 – 12x3
2x3 (6x2 + 5x – 6)=
2x3
= 2(6x + x – x – 6)
–4 9
–6 6
9 4
2x3
= (3x ( 2x + 3) – 2 (2x + 3))
2x3= ((2x + 3) ( 3x – 2))
2x3= (2x + 3) (3x – 2)
Example

7. Slide - 7Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials by Grouping
Factor 12x + 10x – 12x .5 4 3
Check:
32x ( 2x + 3 ) ( 3x – 2 ) 4( 4x ( 3x – 2 )+ 6x )3
5
12x – 8x4
=
= + 18x4
– 12x3
= 12x + 10x – 12x5 4 3
Example (cont)