text: ﻿ Which of the following is/are correct in factorization?
  
  #### Checkbox Question
  
  Which of the following is/are correct in factorization?
  
  1. x^2-6x-16=(x-8)(x+2)
  
  2. ×
  
  x^2y^2-10xy+16=(xy+2)(xy+8)
  
  3. x^2-5xy+6y^2=(x-2)(x-3)
  
  4. ×
  
  x^2+13xy-30y^2=(x-10y)(x-3y)
  
  Collected in the board: Factorization
  
  Steven Zheng posted 2 days ago
  
  1. x^2-6x-16
  
  =x^2-8x+2x-16
  
  =x(x-8)+2(x-8)
  
  =(x-8)(x+2)
  
  Correct
  
  2. x^2y^2-10xy+16
  
  =x^2y^2-8xy-2xy+16
  
  =xy(xy-8)-2(xy-8)
  
  =(xy-2)(xy-8)
  
  Therefore
  
  (xy+2)(xy+8) is not correct
  
  3. x^2-5xy+6y^2
  
  =x^2-3xy-2xy+6y^2
  
  =x(x-3y)-2y(x-3y)
  
  =(x-2)(x-3)
  
  Correct
  
  4. x^2+13xy-30y^2
  
  =x^2-2xy+15xy-30y^2
  
  =x(x-2y)+15y(x-2y)
  
  =(x+15y)(x-2y)
  
  Therefore
  
  (x-10y)(x-3y) is not correct
  
  Steven Zheng posted 2 days ago
  
  Scroll to Top
explanation: The document contains a checkbox question with multiple parts, each part presenting a factorization problem and the corresponding correct or incorrect factorization. The document also includes detailed solutions and explanations for each part, indicating whether the given factorization is correct or not.
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: ﻿ Which of the following is/are correct in factorization?
  
  #### Checkbox Question
  
  Which of the following is/are correct in factorization?
  
  1. x^2-6x-16=(x-8)(x+2)
  
  2. ×
  
  x^2y^2-10xy+16=(xy+2)(xy+8)
  
  3. x^2-5xy+6y^2=(x-2)(x-3)
  
  4. ×
  
  x^2+13xy-30y^2=(x-10y)(x-3y)
  
  Collected in the board: Factorization
  
  Steven Zheng posted 2 days ago
  
  1. x^2-6x-16
  
  =x^2-8x+2x-16
  
  =x(x-8)+2(x-8)
  
  =(x-8)(x+2)
  
  Correct
  
  2. x^2y^2-10xy+16
  
  =x^2y^2-8xy-2xy+16
  
  =xy(xy-8)-2(xy-8)
  
  =(xy-2)(xy-8)
  
  Therefore
  
  (xy+2)(xy+8) is not correct
  
  3. x^2-5xy+6y^2
  
  =x^2-3xy-2xy+6y^2
  
  =x(x-3y)-2y(x-3y)
  
  =(x-2)(x-3)
  
  Correct
  
  4. x^2+13xy-30y^2
  
  =x^2-2xy+15xy-30y^2
  
  =x(x-2y)+15y(x-2y)
  
  =(x+15y)(x-2y)
  
  Therefore
  
  (x-10y)(x-3y) is not correct
  
  Steven Zheng posted 2 days ago
  
  Scroll to Top
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a checkbox question with multiple parts, each part presenting a factorization problem and the corresponding correct or incorrect factorization. The document also includes detailed solutions and explanations for each part, indicating whether the given factorization is correct or not.
  
  Label: multiple-question-and-answer