Answer:
The dimensions of the box are (b+3), (b-2) and (b+2).
Step-by-step explanation:
The volume of a rectangular box is
[tex]V=l\times w\times h[/tex]
The volume of a certain box is
[tex]V=b^3+3b^2-4b-12[/tex]
First of all find the factors of above expression by grouping method.
[tex]V=b^2(b+3)-4(b+3)[/tex]
[tex]V=(b+3)(b^2-4)[/tex]
[tex]V=(b+3)(b^2-2^2)[/tex]
[tex]V=(b+3)(b-2)(b+2)[/tex] [tex][\because a^2-b^2=(a+b)(a-b)][/tex]
Volume of a rectangle is the product of its dimensions, therefore the dimensions of the box are (b+3), (b-2) and (b+2).
