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## #1 2005-09-15 16:45:43

help
Guest

### Factoring (X^2 - 4)

Factoring (X^2 + 4)

I know it can be done.

## #2 2005-09-15 16:47:39

hey
Guest

### Re: Factoring (X^2 - 4)

Back in High School in my Pre Cal class, I was shown how to factor something like

(X^2 + 4)

Now I can't think of a way how to factor it.

## #3 2005-09-16 02:11:51

nu
Guest

### Re: Factoring (X^2 - 4)

if you want to factor x^2-4 is easy: (x^2 - y^2) = (x + y)*(x - y), in your case (x+2)*(x-2)

if you want to factor x^2+4 you have to use Ruffini, or interpret this as (x^2 - y^2). The y in this case would be √-4=j√4:

(x^2-(√-4)^2) = (x + √-4 )*(x - √-4 ) = (x + j√4)*(x - j√4), j indicates it is an imaginary number (j = √-1).

nu

## #4 2005-09-16 06:36:13

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: Factoring (X^2 - 4)

Yeah, always remember the differance of two squares. x[sup]2[/sup] - y[sup]2[/sup] = (x + y)(x - y). Always be on the look out for numbers with integer square roots. For instance x[sup]2[/sup] - 25 =  x[sup]2[/sup] - 5[sup]2[/sup] = (x+ 5)(x-5). Also variables with even exponants other (then zero) can always be converted to a square. x[sup]4[/sup] = (x[sup]2[/sup])[sup]2[/sup]

A logarithm is just a misspelled algorithm.

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## #5 2005-09-16 06:37:17

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: Factoring (X^2 - 4)

I guess [sup] 2 [/sup] doesn't work here. :-(

Hmm... x[sup]2[\sup]

A logarithm is just a misspelled algorithm.

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## #6 2005-09-16 10:59:26

MathsIsFun
Registered: 2005-01-21
Posts: 7,660

### Re: Factoring (X^2 - 4)

LOL, maybe I should put that on my to-do list.

If you don't mind I will experiment with your post using the "math" tag:

mikau wrote:

Yeah, always remember the differance of two squares.

.

Always be on the look out for numbers with integer square roots. For instance

.

Also variables with even exponants other (then zero) can always be converted to a square.

Example of the first one:

``[math]\Large x^2 - y^2 = (x + y)(x - y)[/math]``

Now, using the math tag makes things a *little* slower, so best to use when other options fail. I often just cut and paste the symbols from the top of the forum, but there is no "^4", so that is where the math tag could help.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #7 2005-09-16 12:03:03

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: Factoring (X^2 - 4)

Thanks, man. :-)

A logarithm is just a misspelled algorithm.

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