Question

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

Answer 1

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`.