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kerstie
 3 years 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.
kerstie
 3 years 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.

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Callisto
 3 years ago
Best ResponseYou've already chosen the best response.0Do you know how to factorize a polynomial?

kerstie
 3 years ago
Best ResponseYou've already chosen the best response.0? 2 + 1x for the width

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

eseidl
 3 years ago
Best ResponseYou've already chosen the best response.0You 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

kerstie
 3 years ago
Best ResponseYou've already chosen the best response.0dont I just need to find the height and width

eseidl
 3 years ago
Best ResponseYou've already chosen the best response.0I 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.

eseidl
 3 years ago
Best ResponseYou've already chosen the best response.0I have to head work...good luck!

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0is this calculus or pre calc?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0factors 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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0to graph, i would use this http://www.wolframalpha.com/input/?i=x^35x^2%2B6x+domain+0..2
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