Question

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.

Answer 1

Do you know how to factorize a polynomial?

Answer 2

x(2 + -1x)(3 + -1x)

Answer 3

for the height

Answer 4

?
2 + -1x for the width

Answer 5

Your addition signs are redundant. Just write:\[V(x)=x(2-x)(3-x)\]

Answer 6

ok for the height

Answer 7

and the width 2-1x

Answer 8

and the width 2-1x

Answer 9

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

Answer 10

x

Answer 11

dont I just need to find the height and width

Answer 12

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.

Answer 13

I have to head work...good luck!

Answer 14

is this calculus or pre calc?

Answer 15

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

Answer 16

to graph, i would use this
http://www.wolframalpha.com/input/?i=x^3-5x^2%2B6x+domain+0..2

Answer 17

The volume in cubic feet of a box can be expressed as (x)=x^3-〖6x〗^2+8x , or as the product of three linear factors with integer coefficients.

Answer 18

The volume in cubic feet of a box can be expressed as v(x)=x^3-6x^2+8x , or as the product of three linear factors with integer coefficients.

Answer 19

The volume in cubic feet of a box can be expressed as V(x) = x^3 - 6x^2 + 8x, or as the product of three linear factors with integer coefficients.

Answer 20

The volume in cubic feet of a box can be expressed as (x)=x^3-6x^2+8x , or as the product of three linear factors with integer coefficients.

Answer 21

The volume in cubic feet of a box can be expressed as v(x)=x^3-6x^2+8x , or as the product of three linear factors with integer coefficients.

Answer 22

the volume in cubic feet of a box can be expressed as (x)=x^3-6x^2+8x , or as the product of three linear factors with integer coefficients.

Answer 23

The volume in cubic feet of a box can be expressed as (x)=x^3-〖6x〗^2+8x , or as the product of three linear factors with integer coefficients.

Answer 24

. The volume in cubic feet of a box can be expressed as (x)=x^3-〖6x〗^2+8x , or as the product of three linear factors with integer coefficients.

Answer 25

The volume in cubic feet of a box can be expressed as (x) = x^3 - 6x^2 + 8x, or as the product of three linear factors with integer coefficients.

Answer 26

7. The volume in cubic feet of a box can be expressed as (x)=x^3-〖6x〗^2+8x , or as the product of three linear factors with integer coefficients.

Answer 27

My love with his hair of nightingales\nWith his chest of pigeon flutter, of gray doves preening themselves at dawn\nWith his shoulders of tender balconies h

Answer 28

How does this poem represent a modern version of the blazon?

Answer 29

im gay as Fart

Answer 30

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Answer 31

What number can you multiply by \u2212\u221a2 to get a rational number?\n\nSelect each correct answer.

Answer 32

What number can you multiply by \u2212\u221a2 to get a rational number?\n\nSelect each correct answer.

Answer 33

This is from a test. I need an A+. It is the most important exam out of all of the ones I've done.

Answer 34

really need macro help someone

Answer 35

I have literally went everywhere to find answers but i just can't find the answers can someone plzzz help in need of it i need help with this chart here is

Answer 36

Diana and Joby wrote the following proofs to prove that vertical angles are congruent.

Answer 37

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Answer 38

What do you guys think?