text: # If (x3
  
  If (x - 2) is a factor of the polynomial (x3 + mx2 – x + 6) then it must satisfy it.
  
  So, putting x = 2 the polynomial must be zero.
  
  Putting x = 2 and equating to zero.
  
  = (23 + m22 –2 + 6)
  
  = 4m + 12 = 0
  
  = m = -3
  
  If we divide f(x) = (x3 + mx2 –x + 6) by (x - 3) remainder can be find at value of –
  
  (x - 3) = 0
  
  Or x = 3
  
  So we will put x = 3 in f(x) = (x3 + mx2 – x + 6)
  
  f(3) = (33 + m32 – 3 + 6)
  
  = 30 + 9m
  
  So remainder = 30 + 9m
  
  = 30 + 9(-3) = 30 - 27 = 3
  
  So, r = 3.
  
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explanation: The text extract contains a math problem and its solution. The problem is to find the value of 'm' if (x - 2) is a factor of the polynomial (x^3 + mx^2 – x + 6), and then to find the remainder when the polynomial is divided by (x - 3).
  
  The solution is provided step-by-step, and the final answer is given as \( m = -3 \) and the remainder \( r = 3 \).
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: # If (x3
  
  If (x - 2) is a factor of the polynomial (x3 + mx2 – x + 6) then it must satisfy it.
  
  So, putting x = 2 the polynomial must be zero.
  
  Putting x = 2 and equating to zero.
  
  = (23 + m22 –2 + 6)
  
  = 4m + 12 = 0
  
  = m = -3
  
  If we divide f(x) = (x3 + mx2 –x + 6) by (x - 3) remainder can be find at value of –
  
  (x - 3) = 0
  
  Or x = 3
  
  So we will put x = 3 in f(x) = (x3 + mx2 – x + 6)
  
  f(3) = (33 + m32 – 3 + 6)
  
  = 30 + 9m
  
  So remainder = 30 + 9m
  
  = 30 + 9(-3) = 30 - 27 = 3
  
  So, r = 3.
  
  Rate this question :
  
  How useful is this solution?
  We strive to provide quality solutions. Please rate us to serve you better.
  Related Videos
  Structural Organisation In Animals-I54 mins
  Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
  Dedicated counsellor for each student
  24X7 Doubt Resolution
  Daily Report Card
  Detailed Performance Evaluation
  view all courses
  RELATED QUESTIONS :
  
  In each of the foRD Sharma - Mathematics
  
  In each of the foRD Sharma - Mathematics
  
  When (x31</sRS Aggarwal & V Aggarwal - Mathematics
  
  Find the remaindeRS Aggarwal & V Aggarwal - Mathematics
  
  When p (x) = (x<sRS Aggarwal & V Aggarwal - Mathematics
  
  If p (x) = 2x<supRS Aggarwal & V Aggarwal - Mathematics
  
  If (x3RS Aggarwal & V Aggarwal - Mathematics
  
  When p (x) = x<suRS Aggarwal & V Aggarwal - Mathematics
  
  When p (x) = x<suRS Aggarwal & V Aggarwal - Mathematics
  
  (x +1) is a factoRS Aggarwal & V Aggarwal - Mathematics
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract contains a math problem and its solution. The problem is to find the value of 'm' if (x - 2) is a factor of the polynomial (x^3 + mx^2 – x + 6), and then to find the remainder when the polynomial is divided by (x - 3).
  
  The solution is provided step-by-step, and the final answer is given as \( m = -3 \) and the remainder \( r = 3 \).
  
  Label: question-and-answer