

Factoring Polynomials with Common Monomial Factors
In order to factor polynomials with common monomial factors, we must find the highest monomial factor that will divide exacly
into each term of the polynomial. For example:
Factoring the Difference of Two Squares
Since the product of $x+y$ and $xy$ is $x\xb2y\xb2$, the factors of $x\xb2y\xb2$
are $(x+y)$ and $(xy)$. Therefore $x\xb2y\xb2\; =\; (x+y)(xy)$. In order to factor an expression of
this type, we must find the square root of each term. We then write two factors: one is the sum of the two square roots; the other is the
difference of the two square roots. For example:
Factoring Trinomials of the form $x\xb2+bx+c$
A trinomial of the form $x\xb2+bx+c$ is a quadratic where the coefficient of $x\xb2$ is $1$.
In order to factor an equation of this form, we must first find two binomials that have the following characteristics:
For example, let's factor $x\xb2+7x+10$:
NoteIn steps 2 and 3 above, we could have just as likely had fractional or negative values in the mix. This is a simple example, used to show the process. In actuality, factoring trinomials can become a chore of finding common terms. If factoring takes too long, the trinomial expression can be treated as a quadratic equation in order to find the roots. 

Algebra: Logarithms  Algebra: Quadratic Equations 