Factoring a trinomial

As I said yesterday, I really think factoring comes down to trial and error till the process is internalized. As an example today we will factor trinomials.

Consider

5x² - 8x - 21

This is quite a complicated trinomial to factor, lets start with a guess

First off, we know that to get 5x² we need to multiply 5x and x, so that gives us our first two terms:

(5x + ) (x - )

As a further guess I also alternated the signs.

Now we can try guess what two numbers can multiply to give us -21. How about 7 and -3?

(5x + 7) (x - 3)

Checking with the foil method we get
5x² - 8x - 21