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kerstie
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.
Do you know how to factorize a polynomial?
? 2 + -1x for the width
Your addition signs are redundant. Just write:\[V(x)=x(2-x)(3-x)\]
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
dont I just need to find the height and width
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.
I have to head work...good luck!
is this calculus or pre calc?
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
to graph, i would use this http://www.wolframalpha.com/input/?i=x^3-5x^2%2B6x+domain+0..2