**6.4 - 2013 JUNE Q11**

11) You are given that f(

i) Sketch the graph of

ii) State the roots of f(

iii) You are also given that g(

A) Show that g(

B) Show that g(1) = 0 and hence factorise g(

*x*) = (2*x*– 3)(*x*+ 2)(*x*+ 4)i) Sketch the graph of

*y*= f(*x*). [3]ii) State the roots of f(

*x*– 2) = 0. [2]iii) You are also given that g(

*x*) = f(*x*) + 15A) Show that g(

*x*) = 2*x*^{3}+ 9*x*^{2}– 2*x*– 9. [2]B) Show that g(1) = 0 and hence factorise g(

*x*) completely. [5]