What is the zero factor theorem?

Answer 1

The zero factor theorem is relatively simple.

If you have a a product of two (or more) terms, set to equal zero than one or more of the terms must be zero for the equation to be true.

Example 1:

ab = 0

Either a, b, or a and b must be equal to zero for this equation to be true.

i.e., (0)b = 0; a(0) = 0; (0)(0)=0;

This works with more complex equations as well.

Example 2:

(5 - a)(6 - b)=0
Either 5-a=0, 6-b=0 , or both (5-a) and (6-b) equal zero.

In higher level mathematics this can be very useful, because ex is a constant factor you encounter, but ex can never equal zero. Therefore the other term must be the term that equals zero.

i.e., ex(5-x)=0

ex != 0, therefore: 5-x=0

x=5 is the only value of x that satisfies the equation, thus keeping it true.