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Question 612385: I am needing some help. I am so confused and not even sure where to start. Please show all of your work when providing the answers so that I can fully understand the processes. the volume in cubic work feet of a workshop's storage chest is expressed as the product of three dimensions: V(x)=x^3-5x^2-2x+24. The depth is x+2. I need to 1)fnd the linear expressions with integer coefficients for the other dimensions and 2)if the depth of the chest is 7 feet, what are the other dimensions?
Again, please show your work when providing the answers. Again I don't even know where to start. Thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! the volume in cubic work feet of a workshop's storage chest is expressed as the product of three dimensions: V(x)=x^3-5x^2-2x+24. The depth is x+2. I need to 1)fnd the linear expressions with integer coefficients for the other dimensions and 2)if the depth of the chest is 7 feet, what are the other dimensions?
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V(x)=x^3-5x^2-2x+24. The depth is x+2
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Divide "V(x)" by x+2 using synthetic division:
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-2)....1....-5....-2....24
........1.....-7....12..|..0
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Quotient = x^2-7x+12
Factor the Quotient:
x^2 -7x+12 = (x-3)(x-4)
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The "other" dimensions are (x-3) and (x-4)
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If x+2 = 7 ; x = 5
Then x-3 = 2
And x-4 = 1
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Cheers,
Stan H.
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