How do I use the zero factor property when solving a quadratic equation?

You use the zero factor property after you have factored the quadratic to find the solutions.

It is best to look at an example: #x^2+x-6=0#

This factors into:

#(x+3)(x-2)=0#

We find our solutions by setting each factor to zero and solve:

#x+3=0#
#x=-3#

or

#x-2=0#
#x=2#

Previous answer (I was thinking some more complicated before):

You are not using the words precisely. You use the factor theorem with the factor property. The factor theorem states that if you find a #k# such that #P(k)=0#, then #x-k# is a factor of the polynomial. The factor property states that #k# must a factor of the constant term in #P(x)#.

Having said all that, you wouldn't normally use the factor theorem or factor property to solve a quadratic; they are many used to find factors of higher order polynomials. Once you reduce the higher order polynomial to a quadratic, you use regular factoring methods such as FPS or PFS: Factors, Product, and Sum.

#P(x)=ax^2+bx+c#

The problem with the factor theorem and factor property is that it's not as easy to use when #a!=1#.