Question

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

Answer 1

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.