The volume in cubic feet of a workshop's storage chest can be expressed as the product of it's three dimensions: V(x) = x^3 - 3x^2 - x +3. The depth is x + 1
Help find
a.) Find linear expression with integer coefficients for the other dimensions.
b.) If the depth of the chest is 6 feet, what are the other dimensions.
Please Help me and show your work.

Question

The volume in cubic feet of a workshop's storage chest can be expressed as the product of it's three dimensions: V(x) = x^3 - 3x^2 - x +3. The depth is x + 1 
Help find 
a.) Find linear expression with integer coefficients for the other dimensions.
b.) If the depth of the chest is 6 feet, what are the other dimensions.
Please Help me and show your work.

anonymous · Answer

oh you know synthetic divison

anonymous · Answer

if you have one of the roots you can divide into the polynomial to get a quadratic and solve that

anonymous · Answer

No, I really dont know how to do synthetic divison :/

anonymous · Answer

Oh ok.

anonymous · Answer

well since x + 1 works we should try putting -1 in

anonymous · Answer

$$(-1)^{3} - 3(-1)^{2} - (-1) + 3 = 0$$

anonymous · Answer

c0=f(-1)=0
c1=f'(-1)=8
f_L(x)=8(x+1)

anonymous · Answer

Which is that for a or b ?

anonymous · Answer

a+b(x+1)
so a=0 and b=8

anonymous · Answer

or ax+b
a=8 and b=8

anonymous · Answer

I mean there is two questions, question a and b. I needed both of them explained to me.

anonymous · Answer

on how to find them