If you have difficulty factoring trinomials with lead coefficient 1, then you can try the following approach. Some people call this the “bottoms up” method. Note: ALWAYS remember to factor out the GCF first (it will make all of the numbers smaller and easier to work with)

Given Example:

1. Find ac ac = =

2. Find two factors of ac that since ac =and b=19, we need to find two numbers whose product is and that

add up to b. add up to 19. AND . So the numbers we want are 21 and – 2

3. Divide each number by a note: in this problem a was 6

and reduce the fraction.

4. Write two factors, bringing the

“bottoms up” to be the coefficients

of the variable. Answer:

Remember, if you want to check to see if the trinomial is “factorable”, just check to

see if the discriminant () has a “nice” square root. In our previous example…………

= and so we KNOW that could be factored, it was just a case of figuring out HOW.

You try ……………scroll down the page to see the steps.

ac = =

b=13 and

Dividing each of by 12 and reducing….

Now bring the “bottoms up” to write the factors….

Answer:

Check: