Mathematics

Problem

Consider the polynomial expression

P(k)=3k(k^{2}-12)-5(k^{2}-12).

(i) Factorise

P(k)

completely. (ii) Hence, determine all real values of

k

for which

P(k)=0

. (iii) Verify by direct substitution that each value of

k

obtained in part (ii) satisfies the original expression.