Skip to ContentGo to accessibility page
OpenStax Logo
Algebra 1

Factor Trinomials: Mini-Lesson Review

Algebra 1Factor Trinomials: Mini-Lesson Review

Factor Trinomials: Mini-Lesson Review

Factor Trinomials: Mini-Lesson Review

Mini Lesson Question

Question #2: Factor Trinomials

Factor: y 2 − y − 42 .
  1. ( y − 7 ) ( y − 6 )
  2. ( y + 7 ) ( y + 6 )
  3. ( y + 7 ) ( y − 6 )
  4. ( y − 7 ) ( y + 6 )

Factor Trinomials

Example 1

To factor the trinomial x 2 + 8 x + 12 x 2 + 8 x + 12 , you can reverse the process of FOIL.

The trinomial factors to two binomials of the form ( x + m ) ( x + n ) ( x + m ) ( x + n ) .

  • Using FOIL: ( x + m ) ( x + n ) = x 2 + n x + m x + m n ( x + m ) ( x + n ) = x 2 + n x + m x + m n .
  • Using the distributive property: x 2 + ( n + m ) x + m n x 2 + ( n + m ) x + m n .

Take a look at the trinomial x 2 + 8 x + 12 x 2 + 8 x + 12 :

To factor the trinomial, we need factors of 12, m m and n n , so that the sum, n + m n + m , is 8.

Use a table to find all the different combinations of factors of 12. Then, find the sum of the factors.

Factors of 12 Sum of factors

1 , 12 1 , 12

1 + 12 = 13 1 + 12 = 13

2 , 6 2 , 6

2 + 6 = 8 ✓ 2 + 6 = 8 ✓

3 , 4 3 , 4

3 + 4 = 7 3 + 4 = 7

The numbers 2 and 6 have a product of 12 and a sum of 8. They are the factors we need:

x 2 + 8 x + 12 = ( x + 6 ) ( x + 2 ) x 2 + 8 x + 12 = ( x + 6 ) ( x + 2 )

Example 2

Factor the trinomial x 2 − 5 x − 24 x 2 − 5 x − 24 .

To factor the trinomial, we need factors of -24, m m and n n , so that the sum, n + m n + m is -5.

  • The product of the factors is negative, so the factors must have opposite signs. 
  • The sum is negative, so the negative sign will go with the factor with the greater absolute value.
Factors of 12 Sum of factors

1 , − 24 1 , − 24

2 , − 12 2 , − 12

3 , − 8 3 , − 8

4 , − 6 4 , − 6

1 + ( − 24 ) = − 23 1 + ( − 24 ) = − 23

2 + ( − 12 ) = − 10 2 + ( − 12 ) = − 10

3 + ( − 8 ) = − 5 ✓ 3 + ( − 8 ) = − 5 ✓

4 + ( − 6 ) = − 2 4 + ( − 6 ) = − 2

The numbers 3 and -8 have a product of -24 and a sum of -5.

x 2 − 5 x − 24 = ( x + 3 ) ( x − 8 ) x 2 − 5 x − 24 = ( x + 3 ) ( x − 8 )

Example 3

Factor the trinomial x 2 − 9 x + 18 x 2 − 9 x + 18 .

To factor the trinomial, we need factors of 18, m m and n n , so that the sum, n + m n + m , is -9.

  • The product of the factors is positive, so the factors must have the same signs. 
  • The sum is negative, so both factors are negative.
Factors of 18 Sum of factors

− 1 , − 18 − 1 , − 18

− 2 , − 9 − 2 , − 9

− 3 , − 6 − 3 , − 6

− 1 + ( − 18 ) = − 19 − 1 + ( − 18 ) = − 19

− 2 + ( − 9 ) = − 11 − 2 + ( − 9 ) = − 11

− 3 + ( − 6 ) = − 9 ✓ − 3 + ( − 6 ) = − 9 ✓

The numbers -3 and -6 have a product of 18 and a sum of -9.

x 2 − 9 x + 18 = ( x − 3 ) ( x − 6 ) x 2 − 9 x + 18 = ( x − 3 ) ( x − 6 )

Try it

Factoring Trinomials

Factor the trinomial x 2 + 2 x − 24 x 2 + 2 x − 24 .

Check Your Understanding

Factor: y 2 − 13 y + 36 y 2 − 13 y + 36 .

  1. ( y − 4 ) ( y − 9 ) ( y − 4 ) ( y − 9 )

  2. ( y − 2 ) ( y + 18 ) ( y − 2 ) ( y + 18 )

  3. ( y + 4 ) ( y + 9 ) ( y + 4 ) ( y + 9 )

  4. ( y − 6 ) ( y − 6 ) ( y − 6 ) ( y − 6 )

Video: Factoring Trinomials

Watch the following video to learn more about factoring trinomials.

Khan Academy: Factoring Quadratics

Factoring quadratics as (x+a)(x+b) (example 2) | Mathematics II | High School Math | Khan Academy

PreviousNext
Order a print copy
Citation/Attribution
Reuse and redistribution of this content in digital or print format:
  • This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's prior written permission.
  • This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License, which means that you can reuse and modify the material only for noncommercial purposes, must attribute OpenStax, and must distribute any derivative works under the same license.
  • Any commercial printing of this textbook, including using a local or custom printer, must be approved by OpenStax, and proper citation provided.
  • OpenStax-copyrighted images, activities, assessments, and similar components of this book are subject to the same licensing – CC-BY-NC-SA. They can be used for noncommercial purposes with attribution. Commercial use requires permission.
  • Permission requests: Anyone who intends to incorporate this content (including text, images, and other components) into large language models, use it in AI offerings, use it commercially (including in print), and/or has questions about another use case is welcome to complete our reuse request form.
Attribution information
  • If you are redistributing all or part of this book in a noncommercial print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a noncommercial digital format, then for every page that includes OpenStax content, you must license the derivative work under the same CC-BY-NC-SA license as the original, and include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

The information below includes the information needed to generate citations in most major styles (APA, MLA, etc.); you must reformat and organize the information as needed to fit the requirements of the style. Use the information below to generate a citation. We recommend using a citation tool such as this one.

© Apr 23, 2026 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo, and Rice University name, and Rice University logo trademarks, or wordmarks are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.