This document provides examples of factoring trinomials using the FOIL method. It demonstrates how to factor expressions like 18p^2 + 13p + 2 by finding two binomial factors whose product is the trinomial. The steps shown are finding the two binomial factors, using FOIL to multiply them together, and confirming it yields the original trinomial. Several examples of factoring trinomials with variables like g, n, a, and x are presented.

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 using the FOIL method.
Objectives
13.4 Factoring Trinomials by Using the FOIL
Method

3. Slide - 3Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Note
If the original polynomial has no common factor,
then none of its binomial factors will either.
Factoring Trinomials Using FOIL

4. Slide - 4Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor 18p2 + 13p + 2.
Add.
( + 1 ) ( + 2 )18p p
36p
1p
37p Add.
( + 1 ) ( + 2 )p 18p
2p
18p
20p
Add.
( + 1 ) ( + 2 )9p 2p
18p
2p
20p Add.
( + 1 ) ( + 2 )2p 9p
4p
9p
13p
Check by multiplying.
Factor Trinomials Using FOIL
Example
Look for a sum of +13p.

5. Slide - 5Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor 28g2 + 39g + 5.
Add.
( + 1 ) ( + 5 )28g g
140g
1g
141g Add.
( + 1 ) ( + 5 )g 28g
5g
28g
33g
Add.
( + 1 ) ( + 5 )14g 2g
70g
2g
72g Add.
( + 1 ) ( + 5 )2g 14g
10g
14g
24g
Factor Trinomials Using FOIL
Example
Look for a sum of +39g.

6. Slide - 6Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor 28g2 + 39g + 5.
Add.
( + 1 ) ( + 5 )7g 4g
35g
4g
39g
Check by multiplying.
Factor Trinomials Using FOIL
Example (cont.)
Look for a sum of +39g.

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 Using FOIL
Example
Factor 8n2 – 10n + 3.
Add.
( – 1 ) ( – 3 )8n n
–24n
–1n
–25n Add.
( – 1 ) ( – 3 )n 8n
–3n
–8n
–11n
Add.
( – 1 ) ( – 3 )4n 2n
–12n
–2n
–14n Add.
( – 1 ) ( – 3 )2n 4n
–6n
–4n
–10n
Check by multiplying.Look for a sum of –10n.

8. Slide - 8Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials Using FOIL
Example
Factor 10k2 – 19k + 7.
Add.
( – 1 ) ( – 7 )10k k
–70k
–1k
–71k Add.
( – 1 ) ( – 7 )k 10k
–7k
–10k
–17k
Add.
( – 1 ) ( – 7 )5k 2k
–35k
–2k
–37k Add.
( – 1 ) ( – 7 )2k 5k
–14k
–5k
–19k
Check by multiplying.Look for a sum of –19k.

9. Slide - 9Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials Using FOIL
Example
Factor 36d 2 + 4d – 7.
Add.
( + 1 ) ( – 7 )36d d
–252d
1d
–251d Add.
( + 1 ) ( – 7 )d 36d
– 7d
36d
29d
Add.
( – 1 ) ( + 7 )36d d
252d
–1d
251d Add.
( – 1 ) ( + 7 )d 36d
7d
–36d
–29d
Look for a sum of +4d.

10. Slide - 10Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials Using FOIL
Example (cont.)
Factor 36d 2 + 4d – 7.
Add.
( + 1 ) ( – 7 )18d 2d
–126d
2d
–124d Add.
( + 1 ) ( – 7 )2d 18d
– 14d
18d
4d
Check by multiplying.Look for a sum of +4d.

11. Slide - 11Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomial Using FOIL
Example
Factor 15a2 + 7a – 4.
Add.
( + 1 ) ( – 4 )15a a
–60a
1a
–59a Add.
( + 1 ) ( – 4 )a 15a
– 4a
15a
11a
Add.
( – 1 ) ( + 4 )15a a
60a
–1a
59a Add.
( – 1 ) ( + 4 )a 15a
4a
–15a
–11a
Look for a sum of +7a.

12. Slide - 12Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomial Using FOIL
Example (cont.)
Factor 15a2 + 7a – 4.
Add.
( + 1 ) ( – 4 )5a 3a
–20a
3a
–17a Add.
( + 1 ) ( – 4 )3a 5a
–12a
5a
–7a
Add.
( – 1 ) ( + 4 )5a 3a
20a
–3a
17a Add.
( – 1 ) ( + 4 )3a 5a
12a
–5a
7a
Check by multiplying.Look for a sum of +7a.

13. Slide - 13Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials Using FOIL
Example
Add.
( + 7y ) ( – 5y )3x 4x
–15xy
28xy
13xy
Look for a sum of –13xy.Factor 12x2 – 13xy – 35y2
Add.
( + 7y ) ( – 5y )4x 3x
–20xy
21xy
1xy
Add.
( – 7y ) ( + 5y )3x 4x
15xy
–28xy
–13xy
Check by multiplying.

14. Slide - 14Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Check by multiplying.
Factor Trinomials Using FOIL
Example
Add.
( + 5b ) ( – 3b )8a 3a
–24ab
15ab
–9ab
Look for a sum of +2ab.Factor 24a2 + 2ab – 15b2.
Add.
( + 5b ) ( – 3b )3a 8a
–9ab
40ab
31ab
Add.
( + 5b ) ( – 3b )6a 4a
–18ab
20ab
2ab

15. Slide - 15Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials Using FOIL
Example
Add.
( + 5 ) ( + 2 )6y 3y
12y
15y
27y
Check by multiplying.Look for a sum of +27y.Factor 90y3 + 135y2 + 50y.
90y3 + 135y2 + 50y = 5y (18y2 + 27y + 10)
The completely factored form of 90y3 + 135y2 + 50y is
90y3 + 135y2 + 50y = 5y (6y + 5) (3y + 2)

16. Slide - 16Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Factor Trinomials Using FOIL
Example
Add.
( – 3 ) ( – 2 )7x 2x
–14x
–6x
–20x
Check by multiplying.Look for a sum of –25x.Factor 42x3 – 75x2 + 18x.
42x3 – 75x2 + 18x = 3x (14x2 – 25x + 6)
Add.
( – 3 ) ( – 2 )2x 7x
–4x
–21x
–25x
The completely factored form of 42x3 – 75x2 + 18x is
42x3 – 75x2 + 18x = 3x (2x – 3) (7x – 2)

17. Slide - 17Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Remember to include the common factor in
the final factored form.
CAUTION
Factor Trinomials Using FOIL