# Why Do You Factor Before Finding The Zeros?

• Nov 8th 2011, 09:23 AM
ArcherSam
Why Do You Factor Before Finding The Zeros?
Hey,

I'm just curious why we factor before finding the zeros of an equation. My guess is that it has something to do with the zero product property.

$\begin{array}{l}a + b \ne 0\\ab = 0\end{array}$

Sam
• Nov 8th 2011, 09:47 AM
Deveno
Re: Why Do You Factor Before Finding The Zeros?
in the case of a quadratic, factoring IS finding the zeros: if f(a) = 0, then x - a is a factor, and vice versa.

for higher degree polynomial equations, factoring (if possible) reduces the problem to one that is easier to solve.
• Nov 8th 2011, 10:11 AM
ArcherSam
Re: Why Do You Factor Before Finding The Zeros?
So, by setting f(x) or y equal to zero. It simply stating where y is equal to zero, you can solve for x to find where x will make y equal zero. Thus, satisfying the definition of an zero or x-intercept. I really have to learn the philosophy of math to get how these statements of equality can exist. Thanks again Devano.