If you write a polynomial as the product of two or more polynomials, you have factored the polynomial. Here is an example:[br][br][img width=404,height=23]http://www.sosmath.com/algebra/factor/fac02/img1.gif[/img][br][br]The polynomials [i]x[/i]-3 and [img width=51,height=29]http://www.sosmath.com/algebra/factor/fac02/img2.gif[/img] are called factors of the polynomial [img width=149,height=33]http://www.sosmath.com/algebra/factor/fac02/img3.gif[/img] . Note that the degrees of the factors, 1 and 2, respectively, add up to the degree 3 of the polynomial we started with. Thus factoring breaks up a complicated polynomial into easier, lower degree pieces.[br][br]We are not completely done; we can do better: we can factor[br][br][img width=447,height=24]http://www.sosmath.com/algebra/factor/fac02/img4.gif[/img][br][br]We have now factored the polynomial into three linear (=degree 1) polynomials. 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.