Question

The volume of a rectangular box is found by multiplying its length, width, and height: V = lwh. A certain box has a volume of b 3 + 3b 2 - 4b - 12. Factor the four-term polynomial to find the dimensions of the box. Hint: Use factoring by grouping to factor the four term polynomial first.

Answer 1

i think its (b+3) (b+2) (b-2) maybe wrong not sure

Answer 2

The dimensions of the box are (b+3), (b-2) and (b+2).

Explanation:

The volume of a rectangular box is

`V=l* w* h`

The volume of a certain box is

`V=b^3+3b^2-4b-12`

First of all find the factors of above expression by grouping method.

`V=b^2(b+3)-4(b+3)`

`V=(b+3)(b^2-4)`

`V=(b+3)(b^2-2^2)`

`V=(b+3)(b-2)(b+2)`
`[\because a^2-b^2=(a+b)(a-b)]`

Volume of a rectangle is the product of its dimensions, therefore the dimensions of the box are (b+3), (b-2) and (b+2).