6.5.7 Lesson Summary

In this lesson, you learned how to:

• Factor trinomials of the form $x^2+bx+c$.
• Factor trinomials of the form $a{x}^2+bx+c$ using trial and error.
• Factor trinomials of the form $a{x}^2+bx+c$ using the “$ac$” method.
• Factor using substitution.

Here are the activities that helped you reach those goals:

• 6.5.1: Undoing FOIL
  • In this activity, you learned the steps used to factor a trinomial by reversing the FOIL method.
• 6.5.2: Factoring Trinomials with Leading Coefficients of 1
  • In this activity, you learned how to factor any trinomial of the form $x^2+bx+c$. By finding the factors of the $c$ term and checking to see if they add up to the $b$ term, you are able to find the factors of a trinomial of this form.
  • 6.5.2: Self Check
  • 6.5.2: Additional Resources
• 6.5.3: Factoring Trinomials Using Trial and Error
  • In this activity, you learned that you sometimes need to factor out the GCF from a trinomial as the first step to factoring. You also learned some tricks to help determine the factors of a trinomial, such as when the middle term is negative and the last term is positive, the signs in the binomial factors must both be negative. You practiced finding the factors of a trinomial of the form $a{x}^2+bx+c$ using a trial and error method.
  • 6.5.3: Self Check
  • 6.5.3: Additional Resources
• 6.5.4: Factoring Trinomials Using the “$ac$” Method and Substitution
  • In this activity, you learned a method that can be used to factor any trinomial, the “$ac$” method. By finding two numbers that multiply to $ac$ and add to $b$, you can factor the trinomial by grouping. You also learned a substitution method that allows you to factor trinomials that do not appear to fit into the $a{x}^2+bx+c$ form at first.
  • 6.5.4: Self Check
  • 6.5.4: Additional Resources
• 6.5.5: Choosing Your Own Method to Factor Trinomials
  • In this activity, you combined everything you learned in the lesson to choose your own preferred method to factor a trinomial.

After these activities, you completed the following practice:

• 6.5.6: Practice