text: # 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
explanation: The document is a math forum post where a user named metallica007 asks if their steps for factoring the equation \( Y = x + x^2 - x^4 \) are correct. Another user, Raoh, confirms that the steps are not correct and points out the specific step where the error occurs. Bacterius provides an alternative correct factorization and a method to verify the correctness of the factorization.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a math forum post where a user named metallica007 asks if their steps for factoring the equation \( Y = x + x^2 - x^4 \) are correct. Another user, Raoh, confirms that the steps are not correct and points out the specific step where the error occurs. Bacterius provides an alternative correct factorization and a method to verify the correctness of the factorization.
  
  Label: question-and-answer