Factorizer

Last updated:
20-Mar-2005
Author:
Mooffie

Introduction

Soon after I learnt of Computer Algebra Systems I became fascinated by their abilities. I always believed manipulating algebraic expressions involved art, and I couldn't understand how a computer could be programmed to do art.

Factorizer is my humble attempt at dispelling the magic CAS holds over me. It was also fun to make. Factorizer is a JavaScript application that factors univariate polynomials. If you need to factor multivariate polynomials, or other kinds of expressions, you'll have to resort to a full-blown CAS like this one.

Where is it?

Enter your polynomial in the entry box bellow and hit the "Factor!" button. You can also enter a number to see its prime factors. You may also download Factorizer and use it off-line (see bottom of page for a link and terms of use).

For some example polynomials, .

How does it work?

Factorizer uses three and only three methods for factoring:

1. Recognizing and factoring factors of two special patterns: a(xn)2+bxn+c
2. and (anxn)2-n2.
3. Finding rational roots using the rational roots test. Whenever a root is found the polynomial is divided by (x-x0) using synthetic division. x==0 is also tested.
4. Finding irrational (and, optionally, complex) roots for quadratic factors using the quadratic formula If you choose "Find rational roots only" (above), this method is not used.

Limitations

Factorizer uses only the above three method to factor a polynomial. Therefore, it cannot factor the following polynomials:

• x4 + 1 (no rational roots and the quadratic formula cannot be applied)
• x4 - 8x3 - 16 (ditto)
• x3 + 4 (ditto)

Although Factorizer cannot fully factor all polynomial, at least it can help you reduce their degree.

Input

You can use relaxed syntax when entering polynomials: the operators "*", "^" and "+" can be omitted, and the order of the terms is not important. That is, the polynomial 3x4 - 24x2 + 48 can be entered as:

• 3*x^4 - 24*x^2 + 48
• 3x^4 - 24x^2 + 48
• 3x4 - 24x2 + 48
• 3x4 -24x2 48
• -24x2 48 3x4