Given the polynomial g(x)=x3−4x2−3x+18.
a. (i) Verify that x=3 is a zero of g(x).
b. (ii) Find the quadratic factor obtained when g(x) is divided by (x−3).
c. (iii) Factorise the quadratic found in part (ii) and hence write g(x) in its fully factored form.
d. (iv) State the multiplicity of each zero of g(x).