text: The volume in cubic… - QuestionCove
  OpenStudy (anonymous):
  
  The volume in cubic feet of a box can be expressed as V(x)=x^3-5x^2+6x or as the product of three linear factors with integer coefficients. The width of the box is 2 – x. a. Factor the polynomial to find linear expressions for the height and the width. b. Graph the function. Find the x-intercepts. What do they represent? c. Describe a realistic domain for the function. d. Find the maximum volume of the box.
  
  4 years ago
  OpenStudy (callisto):
  
  Do you know how to factorize a polynomial?
  
  4 years ago
  OpenStudy (anonymous):
  
  x(2 + -1x)(3 + -1x)
  
  4 years ago
  OpenStudy (anonymous):
  
  for the height
  
  4 years ago
  OpenStudy (anonymous):
  
  ? 2 + -1x for the width
  
  4 years ago
  OpenStudy (anonymous):
  
  Your addition signs are redundant. Just write:$V(x)=x(2-x)(3-x)$
  
  4 years ago
  OpenStudy (anonymous):
  
  ok for the height
  
  4 years ago
  OpenStudy (anonymous):
  
  and the width 2-1x
  
  4 years ago
  OpenStudy (anonymous):
  
  and the width 2-1x
  
  4 years ago
  OpenStudy (anonymous):
  
  You know 2-x is the width. Now the length is either x or 3-x. Which one makes sense? Can we decide this with the information we are given
  
  4 years ago
  OpenStudy (anonymous):
  
  x
  
  4 years ago
  OpenStudy (anonymous):
  
  dont I just need to find the height and width
  
  4 years ago
  OpenStudy (anonymous):
  
  I don't see a way to determine this. We can pick 3-x as the length, making x the height. Or we could call 3-x the height and then x is the length. It is arbitrary which one we assign to each dimension since the volume comes out the same regardless of the labels we choose.
  
  4 years ago
  OpenStudy (anonymous):
  
  I have to head work...good luck!
  
  4 years ago
  OpenStudy (anonymous):
  
  is this calculus or pre calc?
  
  4 years ago
  OpenStudy (anonymous):
  
  factors as $x(x-3)(x-2)$ no need for the minus sign. reasonable domain would be something like $$0<x<2$$ because these are lengths and you can't have a negative length
  
  4 years ago
  OpenStudy (anonymous):
  
  to graph, i would use this http://www.wolframalpha.com/input/?i=x^3-5x^2%2B6x+domain+0..2
  
  4 years ago
explanation: The document contains a math question and a series of interactions that partially answer the question. The question is about factoring a polynomial to find the dimensions of a box and further analyzing the function.
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distilabel_metadata.role: system
distilabel_metadata.content: The volume in cubic… - QuestionCove
  OpenStudy (anonymous):
  
  The volume in cubic feet of a box can be expressed as V(x)=x^3-5x^2+6x or as the product of three linear factors with integer coefficients. The width of the box is 2 – x. a. Factor the polynomial to find linear expressions for the height and the width. b. Graph the function. Find the x-intercepts. What do they represent? c. Describe a realistic domain for the function. d. Find the maximum volume of the box.
  
  4 years ago
  OpenStudy (callisto):
  
  Do you know how to factorize a polynomial?
  
  4 years ago
  OpenStudy (anonymous):
  
  x(2 + -1x)(3 + -1x)
  
  4 years ago
  OpenStudy (anonymous):
  
  for the height
  
  4 years ago
  OpenStudy (anonymous):
  
  ? 2 + -1x for the width
  
  4 years ago
  OpenStudy (anonymous):
  
  Your addition signs are redundant. Just write:$V(x)=x(2-x)(3-x)$
  
  4 years ago
  OpenStudy (anonymous):
  
  ok for the height
  
  4 years ago
  OpenStudy (anonymous):
  
  and the width 2-1x
  
  4 years ago
  OpenStudy (anonymous):
  
  and the width 2-1x
  
  4 years ago
  OpenStudy (anonymous):
  
  You know 2-x is the width. Now the length is either x or 3-x. Which one makes sense? Can we decide this with the information we are given
  
  4 years ago
  OpenStudy (anonymous):
  
  x
  
  4 years ago
  OpenStudy (anonymous):
  
  dont I just need to find the height and width
  
  4 years ago
  OpenStudy (anonymous):
  
  I don't see a way to determine this. We can pick 3-x as the length, making x the height. Or we could call 3-x the height and then x is the length. It is arbitrary which one we assign to each dimension since the volume comes out the same regardless of the labels we choose.
  
  4 years ago
  OpenStudy (anonymous):
  
  I have to head work...good luck!
  
  4 years ago
  OpenStudy (anonymous):
  
  is this calculus or pre calc?
  
  4 years ago
  OpenStudy (anonymous):
  
  factors as $x(x-3)(x-2)$ no need for the minus sign. reasonable domain would be something like $$0<x<2$$ because these are lengths and you can't have a negative length
  
  4 years ago
  OpenStudy (anonymous):
  
  to graph, i would use this http://www.wolframalpha.com/input/?i=x^3-5x^2%2B6x+domain+0..2
  
  4 years ago
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a series of interactions that partially answer the question. The question is about factoring a polynomial to find the dimensions of a box and further analyzing the function.
  
  Label: question-and-answer