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 x-2. Factor the polynomial to find linear expressions for the height and the length.

Question

whpalmer4 · Answer

We know that we have three expressions we will multiply together to get a product of $x^3-6x^2+8x$, and that one of the expressions is $x-2$.

I would start by dividing $x^3-6x^2+8x$ by $x-2$, which will give you a quadratic.  Then factor that to get the other two expressions.

vijeya3 · Answer

We have the expression
x^3-6x^2+8x with us.Now we have 'x' common in all the terms.So we would first take 'x' common from the expression.
x(x^2-6x+8)
So we have one of the dimensions as (x-2) and the other as 'x'
We would now factorize the remaining equation-
(x^2-6x+8)
x^2-4x-2x+8
x(x-4)-2(x-4)
(x-2)(x-4)
So,we get the three dimensions of the cuboid as-
x , (x-4) and (x-2)
I hope this is helpful:)

kimjafo · Answer

Thanks to both of you!!