1. ## Common Factor

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

Thank you

2. Originally Posted by metallica007
Hi
For the following equations
$\displaystyle Y=x+x^2-x^4$
do the following steps are correct ?
$\displaystyle x+(x-x^2)(x+x^2)$
$\displaystyle x+x(1-x)(1+x)$
$\displaystyle x[1+1-x^2]$
$\displaystyle x[2-x^2]$

Thank you
that's not correct.

3. No. The common factor is just $\displaystyle x$.

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

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

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

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

Take $\displaystyle x = 2$. Thus we get :

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

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

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

4. Originally Posted by metallica007
Hi
For the following equations
$\displaystyle Y=x+x^2-x^4$
do the following steps are correct ?
$\displaystyle x+(x-x^2)(x+x^2)$
$\displaystyle x+x(1-x)(1+x)$ <.... here's your problem
(what follows is wrong)
$\displaystyle x[1+1-x^2]$
$\displaystyle x[2-x^2]$

Thank you
$\displaystyle x+(x-x^2)(x+x^2)=x+x^2(1-x)(1+x)=x(1+x(1-x)(1+x))$

5. Originally Posted by Raoh
$\displaystyle x+(x-x^2)(x+x^2)=x+x^2(1-x)(1+x)=x(1+x(1-x)(1+x))$
Thank you for show me the problem
I was not sure about that step