# Factoring

Some polynomials have special forms. In this case we have formulas we can
use to do
the factoring

If a problem cannot be factored then we say that it is prime.

Definition 0.1 Difference of Squares
If A and B are real numbers , variables , or algebraic expressions, then

Example 0.1 Difference of Square

where A = x and B = 4.

where A = 2x and B = 3.

where A = xy and B = 10.

where A = 5x2 and B = 3y3.

where A = x - 6 and B = y.

Sometimes after an expression is factored , more factoring will need to be
done. Always check that the expression cannot be factored any further.

Example 0.2 Repeated Factoring

where A = x2 and B = 1.

But notice one of the factors is again a difference of squares .

Definition 0.2 Sum/Difference of Cubes

1. Factoring the Sum of Cubes

2. Factoring the Difference of Cubes

To remember the signs recall SOAP. Stands for same, opposite, always
positive .

First signs are same, next is opposite the first, last sign is always positive .

Example 0.3 Sum/Difference of Cubes

where A = x and B = 1

where A = x and B = 10

where A = 3x and B = 2

where A = xy and B = 4

where A = 6 and B = x

so

Property 0.1 Factoring Perfect Square Polynomials

Trinomials obtained from squaring a binomial are called perfect square tri-
nomials and have a special form.

so

and

so

Example 0.4 Perfect Square Trinomial

If this is a perfect square trinomial then A = x and B = 1 making
2AB = 2(x)(1) = 2x which it is.
So this is a perfect square trinomial.

If this is a perfect square trinomial then A = x and B = 7 making
2AB = 2(x)(7) = 14x which it is.
So this is a perfect square trinomial.

If this is a perfect square trinomial then A = 5y and B = 1 making
2AB = 2(5y)(1) = 10y which it is.
So this is a perfect square trinomial.

If this is a perfect square trinomial then A = 3x and B = 8y making
2AB = 2(3x)(8y) = 48xy which it is.
So this is a perfect square trinomial.

 Prev Next

Start solving your Algebra Problems in next 5 minutes!

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of June 22nd 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 tutor.com 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...)

ORDER NOW!