Question

The volume of a box V, varies with some variable x as V(x) = x³-12x²+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

$$V(x)=x^3 - 12x ^2 + 44x -48$$ $$x^3 - 12x ^2 + 44x -48 =x^2(x-2)-10x(x-2)+24(x-2)$$ $$=x^2(x-2)-10x(x-2)+24(x-2)$$ $$=(x-2)(x^2-10x+24)$$ $$=(x-2)(x-4)(x-6)$$ $$a_1=2, a_2=4, a_3=6$$ $$a\in\{2,4,6\}$$