Common Factor

**metallica007** · December 26th 2009, 12:32 PM

Hi
For the following equations
$Y=x+x^2-x^4$
do the following steps are correct ?
$x+(x-x^2)(x+x^2)$
$x+x(1-x)(1+x)$
$x[1+1-x^2]$
$x[2-x^2]$

Thank you

**Raoh** · December 26th 2009, 01:34 PM

Originally Posted by metallica007

Hi
For the following equations
$Y=x+x^2-x^4$
do the following steps are correct ?
$x+(x-x^2)(x+x^2)$
$x+x(1-x)(1+x)$
$x[1+1-x^2]$
$x[2-x^2]$

Thank you

that's not correct.

**Bacterius** · December 26th 2009, 01:34 PM

No. The common factor is just $x$ .

$Y=x+x^2-x^4$

$Y = x(1 + x - x^3)$

--------------

When you are unsure about a result, just try with some numbers. With your result, what you are saying is that :

$x + x^2 - x^4 = x(2 - x^2)$

Take $x = 2$ . Thus we get :

$2 + 2^2 - 2^4 = 2(2 - 2^2)$

And therefore your results suggests that $-10 = -4$

But $-10 \neq -4$ , thus your result is wrong.

**Raoh** · December 26th 2009, 01:40 PM

Originally Posted by metallica007

Hi
For the following equations
$Y=x+x^2-x^4$
do the following steps are correct ?
$x+(x-x^2)(x+x^2)$
$x+x(1-x)(1+x)$ <.... here's your problem
(what follows is wrong)
$x[1+1-x^2]$
$x[2-x^2]$

Thank you

$x+(x-x^2)(x+x^2)=x+x^2(1-x)(1+x)=x(1+x(1-x)(1+x))$

**metallica007** · December 26th 2009, 02:39 PM

Originally Posted by Raoh

$x+(x-x^2)(x+x^2)=x+x^2(1-x)(1+x)=x(1+x(1-x)(1+x))$

Thank you for show me the problem
I was not sure about that step

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