Mathematics

Problem

Let

p(x)=2x^{3}+3x^{2}+kx+6

. a. (i) Find the value of

k

x+2

is a factor of

p(x)

. b. (ii) For the value of

k

obtained in part (i), divide

p(x)

x+2

and write down the quadratic quotient. c. (iii) Hence factorise

p(x)

completely and write all its zeros.