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

2. Example 1
Factor:
Determine the value of ac.
Write a trinomial in the
form of x2+bx+ac.
We already know how to factor trinomials of this form.

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

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

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

6. The trinomial is factored using

7. Example 2
Factor:
Determine the value of ac
Write a trinomial in the
form of x2+bx+ac.

8. 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
Sum of Factors
Start with larger numbers since we know (-1)(-420) won’t even be close.

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

10. Reduce the fractions.
Complete using the “bottoms up” step

11. The trinomial is factored using

12. Example 3
Factor:
Determine the value of ac
Write a trinomial in the
form of x2+bx+ac.

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

14. Reduce the fractions.
Complete using the “bottoms up” step

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

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

17. Factor:
Factor the GCF
Now factor the trinomial factor
Determine the value of ac
Write a trinomial in the
form of x2+bx+ac.

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

19. Reduce the fractions.
Complete using the “bottoms up” step

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

21. The trinomial is factored using

22. END OF PRESENTATION