text: # How do you factor completely 45t^4 - 90t^3 + 25t^2?
  
  Apr 18, 2016
  
  Just to clarify what the other contributor was saying...
  
  #### Explanation:
  
  Factor out the GCF.
  
  $5 {t}^{2} \left(9 {t}^{2} - 18 t + 5\right)$
  
  The expression inside the parentheses can be factored as a trinomial of the form $y = a {x}^{2} + b x + c , a \ne 1$. To do this, we must find two numbers that multiply to $a \times c$ and that add to b, and then follow the following process. Two numbers that do this are -15 and -3.
  
  $5 {t}^{2} \left(9 {t}^{2} - 3 t - 15 t + 5\right)$
  
  $5 {t}^{2} \left(3 t \left(3 t - 1\right) - 5 \left(3 t - 1\right)\right)$
  
  $5 {t}^{2} \left(3 t - 5\right) \left(3 t - 1\right)$
  
  This is completely factored.
  
  Hopefully this helps!
explanation: The document contains a math question and a detailed explanation of how to solve it. The question is about factoring the polynomial \(45t^4 - 90t^3 + 25t^2\), and the answer provides a step-by-step process to factor it completely.
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: # How do you factor completely 45t^4 - 90t^3 + 25t^2?
  
  Apr 18, 2016
  
  Just to clarify what the other contributor was saying...
  
  #### Explanation:
  
  Factor out the GCF.
  
  $5 {t}^{2} \left(9 {t}^{2} - 18 t + 5\right)$
  
  The expression inside the parentheses can be factored as a trinomial of the form $y = a {x}^{2} + b x + c , a \ne 1$. To do this, we must find two numbers that multiply to $a \times c$ and that add to b, and then follow the following process. Two numbers that do this are -15 and -3.
  
  $5 {t}^{2} \left(9 {t}^{2} - 3 t - 15 t + 5\right)$
  
  $5 {t}^{2} \left(3 t \left(3 t - 1\right) - 5 \left(3 t - 1\right)\right)$
  
  $5 {t}^{2} \left(3 t - 5\right) \left(3 t - 1\right)$
  
  This is completely factored.
  
  Hopefully this helps!
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed explanation of how to solve it. The question is about factoring the polynomial \(45t^4 - 90t^3 + 25t^2\), and the answer provides a step-by-step process to factor it completely.
  
  Label: question-and-answer