Question

The volume of a box V, varies with some variable x as V(x)=x^3 - 12x ^2 + 44x -48 cubic metres. If (x - a) metre is the measurement of one side of the box, then find the value for a.

Answer 1

$$V(x)=x^3 - 12x ^2 + 44x -48$$

$$x^3 - 12x ^2 + 44x -48 =x^2(x-2)-10x(x-2)+24(x-2)$$

$$=x^2(x-2)-10x(x-2)+24(x-2)$$

$$=(x-2)(x^2-10x+24)$$

$$=(x-2)(x-4)(x-6)$$

$$a_1=2, a_2=4, a_3=6$$

$$a\in\{2,4,6\}$$