Factoring Trinomials a 1 Bottoms Up Method This

Factoring – Trinomials (a ≠ 1), Bottoms Up Method • This is the third method shown for factoring • The two previous methods shown were 1. Guess and Check 2. ac. • You only need to know one of the three methods! • Bottoms Up will be explained using an example.

• Example 1 Factor: 1. Determine the value of ac. 2. Write a trinomial in the form of x 2+bx+ac. We already know how to factor trinomials of this form.

Since b=17 is positive, let the negative factor be the smaller of the two numerical values. Factors of -60 Sum of Factors

3. Write two factors using the two numbers. 4. Divide the two numbers by the value of a in the original trinomial.

5. Reduce the fractions. 6. Complete using the “bottoms up” step

The trinomial is factored using

• Example 2 Factor: 1. Determine the value of ac 2. Write a trinomial in the form of x 2+bx+ac.

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. Sum of Factors

3. Write two factors using the two numbers. 4. Divide the two numbers by the value of a in the original trinomial.

5. Reduce the fractions. 6. Complete using the “bottoms up” step

The trinomial is factored using

• Example 3 Factor: 1. Determine the value of ac 2. Write a trinomial in the form of x 2+bx+ac.

3. Factor 4. Divide the two numbers by the value of a in the original trinomial.

5. Reduce the fractions. 6. Complete using the “bottoms up” step

Do you see the error? This is not the same as the original trinomial!

Note that the original trinomial has a common factor. IMPORTANT: you must factor the GCF before using Bottoms Up. Let’s redo the problem.

Factor: Factor the GCF Now factor the trinomial factor 1. Determine the value of ac 2. Write a trinomial in the form of x 2+bx+ac.

3. Factor 4. Divide the two numbers by the value of a in the original trinomial.

5. Reduce the fractions. 6. Complete using the “bottoms up” step

7. Back to the original where we took out the GCF. 8. Write in the binomial factors.

The trinomial is factored using