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The volume in cubic feet of a box can be expressed as V(x)=x^35x^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 xintercepts. What do they represent?
c. Describe a realistic domain for the function.
d. Find the maximum volume of the box.
 one year ago
 one year ago
The volume in cubic feet of a box can be expressed as V(x)=x^35x^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 xintercepts. What do they represent? c. Describe a realistic domain for the function. d. Find the maximum volume of the box.
 one year ago
 one year ago

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CallistoBest ResponseYou've already chosen the best response.0
Do you know how to factorize a polynomial?
 one year ago

kerstieBest ResponseYou've already chosen the best response.0
? 2 + 1x for the width
 one year ago

eseidlBest ResponseYou've already chosen the best response.0
Your addition signs are redundant. Just write:\[V(x)=x(2x)(3x)\]
 one year ago

eseidlBest ResponseYou've already chosen the best response.0
You know 2x is the width. Now the length is either x or 3x. Which one makes sense? Can we decide this with the information we are given
 one year ago

kerstieBest ResponseYou've already chosen the best response.0
dont I just need to find the height and width
 one year ago

eseidlBest ResponseYou've already chosen the best response.0
I don't see a way to determine this. We can pick 3x as the length, making x the height. Or we could call 3x 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.
 one year ago

eseidlBest ResponseYou've already chosen the best response.0
I have to head work...good luck!
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
is this calculus or pre calc?
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
factors as \[x(x3)(x2)\] 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
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
to graph, i would use this http://www.wolframalpha.com/input/?i=x^35x^2%2B6x+domain+0..2
 one year ago
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