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

1 Answer
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=0x2+x6=0

This factors into:

(x+3)(x-2)=0(x+3)(x2)=0

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

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

or

x-2=0x2=0
x=2x=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 kk such that P(k)=0P(k)=0, then x-kxk is a factor of the polynomial. The factor property states that kk must a factor of the constant term in P(x)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+cP(x)=ax2+bx+c

The problem with the factor theorem and factor property is that it's not as easy to use when a!=1a1.