{{Merge to|#redirect[[Factorization of polynomials|date=May 2010}}]]
{{Orphan|date=April 2010}}
{{Cleanup|date=May 2010}}
The methods that are used to factor a polynomial depend on how many terms the polynomial has.<br /> Note: This page assumes that the polynomials are being factored on the real field (that the coefficients of the factors are real numbers).
==Any polynomial==
The first step to factor '''any''' polynomial is '''always''' to factor out the '''Greatest Common Factor''', commonly referred to as the '''GCF'''.
where <math>(e)(d)=c</math> and <math>d+e=b</math>.
'''For example:'''<br />
<math>x^2-x-6=(x-3)(x+2)</math> because <math>(-3)(2)=-6</math> and <math>-3+2=-1</math><br />
<br />or
<math>x^2-11x+24=(x-3)(x-8)</math> because <math>(-3)(-8)=24</math> and <math>-3+-8=-11</math>
===Non-monic trinomials===
A non-monic trinomial has a constant other than 1 as the leading coefficient.
<math>ax^2+bx+c=(mx+p)(nx+q)</math><br />
where <math>mn=a</math>, <math>pq=c</math>, and <math>mq+pn=b</math>
Many times students are taught that to factor a non-monic trinomials, they must guess different combinations of m,n,p,and q and then [[FOIL method|FOIL]] the factors to see if they had guessed correctly. There is a method of factoring that, while not often taught, will work.
Some polynomials with four terms can be factored by some form of grouping. There are special groupings but the most common form is referred to as '''factoring by grouping''' and is described step by step below.
