1. ## Common Factor

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

2. 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.

3. 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.

4. 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
$x+(x-x^2)(x+x^2)=x+x^2(1-x)(1+x)=x(1+x(1-x)(1+x))$

5. 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