Volume and Factoring Help...?

Question

A certain box has a volume of b^3 + 3b^2 -4b - 12. Factor the four term polynomial to find the Length, Width, and height of the box.


Thanks to anyone who can answer this... it's been really confusing.

Answer 1

b^3+3b^2-4b-12
=b^2(b+3)-4(b+3)
=(b+3)(b^2-4)
=(b+3)(b+2)(b-2)
Any of these can be termed as length width or height of the box but as per convention,the biggest one i.e. b+3 is taken as height,b+2 as the width and b-2 as the height

Answer 2

This polynomial can be factored by grouping:
Look at the first two terms: b^3 + 3b^2
factor this into b^2 * (b+3)
Look at the next two terms: -4b - 12
factor this into -4 * (b+3)
Thus the polynomial can be factored into
(b^2-4)(b+3), which can further be factored into
(b+2)(b-2)(b+3)
As to which one is length, width, and height, your guess is as good as mine!

Answer 3

V = b².(b + 3) - 4.(b + 3)
V = (b + 3).(b² - 4)
V = (b + 3).(b - 2).(b + 2)

Answer 4

b^2(b+3) -4(b+3) and since (b+3) is a common factor

(b+3)(b^2-4) Differebce of squares

(b+3)(b-2)(b+2) where b>2