Question

The volume of a box V

V, varies with some variable x

x as V(x)=x^3 - 12x ^2 + 44x -48

V(x)=x3

−12x2

+44x−48 cubic metres. If (x - a)

(x−a) metre is the measurement of one side of the box, then find the value for a

a.

Answer 1

$$V(a)=a^3-12a^2+44a-48=0$$

$$a^3-2a^2-10a^2+20a+24a-48=0$$

$$a^2(a-2)-10a(a-2)+24(a-2)=0$$

$$(a-2)(a^2-10a+24)=0$$

$$(a-2)(a-4)(a-6)=0$$

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