Question

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. The width of the box is 2 – x.

Factor the polynomial to find linear expressions for the height and the length

Answer 1

you'll have to divide\[\large x^3-(6x)^2+8x\]by 2-x

Using polynomial long division or synthetic division.

Answer 2

How do i do that?

Answer 3

it's gonna be difficult to explain here, this prob is better https://www.youtube.com/watch?v=l6_ghhd7kwQ

Answer 4

ok

Answer 5

I'm guessing it's actually \[\large x^3-6x^2+8x\]
you don't need long division actually. Factor out an x:
\[\large x( x^2-6x+8)\]then you can just factor
\[\large x( x-2)(x-4)\]

since they told you one factor was 2-x, pull out a factor of -1 out of x-2:
\[\large -x( 2-x)(x-4)\]

height and length are the -x and x-4