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

Aug 18, 2014

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:

$\left(x + 3\right) \left(x - 2\right) = 0$

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 $P \left(k\right) = 0$, then $x - k$ is a factor of the polynomial. The factor property states that $k$ must a factor of the constant term in $P \left(x\right)$.

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.

$P \left(x\right) = a {x}^{2} + b x + c$

The problem with the factor theorem and factor property is that it's not as easy to use when $a \ne 1$.