Factoring Trinomials a 1 ac Method The previous

Factoring – Trinomials (a ≠ 1), ac Method • The previous slideshow demonstrated how to use the Guess and Check method to factor trinomials of the form • Another method for factoring these trinomials is called the ac method (also called the grouping method). • The idea is to write the middle term of the trinomial as two terms in such a way that the grouping method can be used to finish the factoring. Table of Contents

ac Method 1. Determine the value of ac 2. Find factors of ac whose sum is b 3. Rewrite the trinomial, where the term bx is written as two terms using step 2 4. Factor using the grouping method Table of Contents

• Example 1 Factor: 1. Determine the value of ac 2. Find factors of ac whose sum is b In this case we would like to find two factors of -60 whose sum is +17. To get -60 the factors will have to be opposite is sign. Table of Contents

Since b=17 is positive, let the negative factor be the smaller of the two numerical values. Factors of -60 Sum of Factors It is of course faster if the above work can be completed in your head. Table of Contents

3. Rewrite the trinomial, where the term bx is written as two terms using step 2 Table of Contents

4. Factor using the grouping method Table of Contents

The trinomial is factored using Table of Contents

• Example 2 Factor: 1. Determine the value of ac 2. Find factors of ac whose sum is b In this case we would like to find two factors of 420 whose sum is -43. Table of Contents

To multiply and get 420 which is positive, the factors will need to be the same sign. To add to -43 means they will both be negative. Factors of 420 Start with larger numbers since we know (-1)(-420) won’t even be close. Table of Contents Sum of Factors

3. Rewrite the trinomial, where the term bx is written as two terms using step 2 Table of Contents

4. Factor using the grouping method Table of Contents

The trinomial is factored using Table of Contents

Table of Contents