Your Algebra Homework Can Now Be Easier Than Ever!


Activity #27 Factoring using the BOX Math 70

Your Name:
Partner(s): 1.

Over the next few days, factoring polynomials is our focus . Unfortunately, no magic wand or
algorithm exists for factoring polynomials. However, one method that some students find
particularly useful is the box method. Here’s how it works. Suppose we begin with a quadratic
polynomial in factored form (x + 2)(x + 4). We can represent the product as the area of a
rectangle of length x + 2 and width x + 4.

By combining the two linear terms on the diagonal, we get the product x2 + 6x + 8.

For factoring, we want to work backwards. We begin by placing the quadratic term x 2 and the
constant term 8 in the upper left box and lower right box, respectively.

Next, we are trying to find the two terms that will go in the upper right and lower left. To do
this we will use another schematic, the DIAMOND. In the top of the diamond we place the
product of the first term and the last, (x2)(+8)= 8x2. In the bottom we place the middle term,

We are looking for the two terms whose product is 8x2 and whose sum is 6x. You can start the
search by looking at possible factors of 8x2. These two terms are placed in the sides of the
diamond and also give us the terms to fill in the box.

Now we continue by factoring out the greatest common factor (GCF) of the terms in the first
row (or the first column):

Then we ask what times x will be x2 which gives the term above the first column, and what times
x will be 4x which gives the term above the second column.

Then fill in the term left of the bottom row in a similar manner.

This will give the factored result.
x2 +6x + 8 = (x + 2)(x + 4)
Task 1: Factoring Trinomials of the Form x2 + bx + c Factor the following quadratic
trinomials using the box :

Task 2: Factoring the Difference of Squares and Perfect Squares The box can be used
to factor differences of squares and perfect squares where the leading coefficient is not 1.
Here, the diamond may not be very useful Instead, try to guess what term times itself will give
the first term and what times itself (or its opposite) will give the last term. Try these.

Task 3: Factoring Trinomials of the Form ax2 + bx + c These can be a little more tricky to
do using the box, but the diamond can help. In fact, for these problems, using the box serves
more as a way of organizing our work so that we avoid making errors. For example, try the next
four examples:

But sometimes, there are many choices. These examples might take a few tries
before you get it right:

Task 4: Simple Factoring First, then the Box Finally, the four examples below remind us
that factoring out a GCF first can make the factoring process much simpler.


Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

OR is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for visitors -- if you order Algebra Helper by midnight of January 21st you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)


Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

OR is an authorized reseller
of goods provided by Sofmath
Check out our demo!
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2021, Algebra-Answer.Com.  All rights reserved.