If you write a polynomial as the product of two or more polynomials, you have factored the polynomial. Thus factoring breaks up a complicated polynomial into easier, lower degree pieces.
Linear polynomials are the easiest polynomials.
We can't do any better. Whenever we cannot factor any further, we say we have factored the polynomial completely . Roots of polynomials. An intimately related concept is that of a root , also called a zero , of a polynomial. Note that is a factor of .