Solving quadractics by factoring

One way to solve a quadratic equation like:

(4x² - 4)=0 is by factoring and setting both factors equal to zero. Because a quadratic contains a x² they often have two solutions.

(4x² - 4)=0 can be factored to

(2x - 2)(2x + 2)=0

Now set both factors equal to zero

2x-2=0
2x+2=0

we get
x=1 and x=-1
substituting 1 or -1 for x will solve the quadratic equation (4x² + 4)=0

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