How to factor Quadratic Equations
and using the Zero Product Property

Factoring Quadratic Equations x²+bx+c
Factor x²-12x-28
To factor x²-12x-28 you must find factors of -28 that will have a sum of -12
x^2_-12x-28=(x+m)(x+n)=x²+(m+n)x+mn
mn=-28
m+n=-12

Factors of -28(mn)	Sum(m+n)
-1,28	27
1,-28	-27
-2,14	12
2,-14	-12
-4,7	3
4,-7	-3

Now put the two factors into the (x+m)(x+n)
x²-12x-28=(x+2)(x-14)


Factoring a trinomial of the form ax²+bx+c
Factor 2x²+7x+3
You would do the same factoring as usual, but since now a=2 you need to factor both a and c
So in equation form it would be in (kx+m)(lx+m) where k and l are factors of a

I would use a 2x2 chart to help solve these kind of equations
On the top right and side of box 1 would be the factors of a
On the top left of box 2 and the side of box 3 would be the factors of c
This is just like a chart so you should just multiply 2x and 3 then 1 and x

then

Then the one on the side should make an equation like this: 2x+1 and the top x+3
then there is your factor 2x²+7x+3=(2x+1)(x+3)

note
If the factoring chart doesn't work,
then I suggest you switch the numbers
around, but only one side
If that doesn't work try other numbers
or your equation is not factorable!

Zero Product Property
Let A and B be real numbers or algebraic expressions. If AB=0, then A=0 and B=0
Same from last example

x²-12x-28=(x+2)(x-14)=0
Separate the two factored answers as if they were equations
So it would be like this x+2=0 and x-14=0 and you want to solve for x
x=-2 or x=14 and that would be the answer

Practice
Factor
1. x²+5x+4
2. x²+13x+40
3. 3k²+32k-11
4.18n²+9n-14
Solve
5.x²-3x-4=0
6.5x²-13x+6=0