Consider the polynomial expression P(k)=3k(k^ 2 -12)-5(k^ 2 -12)

MATHEMATICS · Subjective · AoPS · Mathematics · Follow the Rules · Follow the Rules

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.