Try the Free Math Solver or Scroll down to Tutorials!












Please use this form if you would like
to have this math solver on your website,
free of charge.

Todayยดs Goal: We describe various methods to factor algebraic expressions (specifically
polynomials) as a product of simpler ones.


We have used the distributive property to "expand" algebraic expressions (see Activity 5).
We sometimes need to reverse this process by "factoring" an expression as a product of simpler ones.

Common Factors: The easiest type of factoring occurs when the terms have a common factor.
Example 1: Factor out the common factor in each of the following expression:

Factoring Trinomials: To factor a trinomial of the form

we need to choose numbers r and s so that r + s = b and r s = c .

Example 2: Factor the following trinomials:

we need to choose numbers p, q, r  and  s so that p q = a, r s = c, and  q r + p s = b.
That is, p and q are factors of a whereas r and s are factors of c.

Example 3: Factor the following trinomial:

Special Factoring Formulas:
The first three formulas below are simply Special Product Formulas written backward.
If A and B are any real numbers or algebraic expressions, then:

Example 4: Use a Factoring Formula to factor the following expressions:


Factoring by Grouping Terms:
Polynomials with at least four terms can sometimes be factored by grouping terms.

Example 5: Factor the following expressions by grouping terms:

Factoring an Expression Completely:
When we factor an expression, the result can sometimes be factored further. We repeatedly use the methods
outlined in this activity until we have factored our algebraic expression completely.

Example 6: Factor the following expressions completely:


This last problem is trickier! (Hint: add and subtract "4x2" what do you obtain?)

Example 7 (Mowing a Field):
A square field in a certain state park is mo wed around the edges every week. The rest of the field is kept
unmowed to serve as a habitat for the birds and small animals. the field measures b feet by b feet, and the mowed
strip is x feet wide.

(a) Show that the area of the mowed portion is b2-(b-2x)2.

(b) Factor the expression in (a) to show that the area of the mowed portion is also 4x(b-x).