How does the zero factor property relate to factoring a polynomial?

1 Answer
Sep 24, 2015

Answer:

Well, if you a polynomial is factorable then its roots/zeroes can be easily found by setting it to zero and using the zero factor property. Please see explanation below.

Explanation:

The Zero Product Property:
A product of factors is zero if and only if one or more of the factors is zero. Or:
if #a*b = 0#, then either #a = 0# or #b = 0# or both.
Example: Find the roots of the polynomial by factoring:
#P(x) = x^3-x^2-x+1#, set to zero:
#x^3-x^2-x+1=0#, factor by grouping:
#x^2(x-1)-1(x-1)=0#
#(x^2-1)(x-1)=0#, use difference of squares to factor further:
#(x+1)(x-1)(x-1)=0#, use the zero factor property:
#x+1=0=>x=-1#
#x-1=0=>x=1#
Notice that #x = 1# has a multiplicity of 2.