# Common Factor

• Dec 26th 2009, 12:32 PM
metallica007
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
• Dec 26th 2009, 01:34 PM
Raoh
Quote:

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.(Nerd)
• Dec 26th 2009, 01:34 PM
Bacterius
No. The common factor is just \$\displaystyle x\$.

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

\$\displaystyle 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 :

\$\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.
• Dec 26th 2009, 01:40 PM
Raoh
Quote:

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))\$
• Dec 26th 2009, 02:39 PM
metallica007
Quote:

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
The text passage contains a mathematical question regarding the correctness of a series of algebraic manipulations. It also includes responses that provide an answer to the question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Common Factor

• Dec 26th 2009, 12:32 PM
metallica007
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
• Dec 26th 2009, 01:34 PM
Raoh
Quote:

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.(Nerd)
• Dec 26th 2009, 01:34 PM
Bacterius
No. The common factor is just \$\displaystyle x\$.

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

\$\displaystyle 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 :

\$\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.
• Dec 26th 2009, 01:40 PM
Raoh
Quote:

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))\$
• Dec 26th 2009, 02:39 PM
metallica007
Quote:

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
user
The text passage contains a mathematical question regarding the correctness of a series of algebraic manipulations. It also includes responses that provide an answer to the question.

TYPE: SINGLE_QUESTION_WITH_ANSWER