A square sheet of metal has side (x+6)cm. Squares of side 2cm are cut from each corner and the sides are folded up to make an open box.
(i) Show that the volume V(x) of the box, in cubic centimetres, can be expressed as a polynomial in x.
(ii) Simplify this polynomial completely.
(iii) Factorise the simplified volume polynomial.
(iv) Using your factorisation, find all positive integral values of x (in cm) for which the volume would be zero.
a. (i) Derive volume expression.
b. (ii) Simplify.
c. (iii) Factorise.
d. (iv) Integral values giving zero volume.