Polynomial Division and Factorization  Reducing a Polynomial 
Exercise 5
Given x=2 is a zero of f(x), show that f(x) = x^{3}  3x^{2}
 4x + 12 may be factored as (x  2)(x^{2}  x 6), the
other two zeros are x=3 and x=2, and the complete factorization in
terms of linear factors is f(x)=(x2)(x3)(x+2). The justification
has been given  no further justification is needed.
STATEMENT 
JUSTIFICATION 
x=2 is a zero of f(x) = x^{3}
 3x^{2}  4x + 12

Given Use
Synthetic Division, Properties of Zeros, the Zero Product Rule,
Distributive Property (to factor), and Addition Properties of
Equality.

