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

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

ankitshaw · Answer

is it  6x^2 or (6x)^2 because i can factorise it when its 6x^2

ankitshaw · Answer

(2-x)(4-x)x = f(x)

ankitshaw · Answer

so if width is given by (2-x)  ... then (4-x) and x will give height and length or vice-versa

anonymous · Answer

I will assume the brackets don't exist, because if they did you would have 2 roots, not three and the equation doesn't work..... 

Factor out x
$$x(x^2 -6x +8)$$
Factor this second part again.
(x-2)(x-4)x

Another way to do this (which may help if you don't have such nice numbers) is when they provide a factor of the polynomial, you can divide by that factor to safely simplify the polynomial.