The graph of a polynomial p(x) cuts the x–axis at x=−3,1,2 and meets the y–axis at the point (0,6).
Solve the following sub-questions.
(i) Determine, with working, the simplest possible algebraic expression for p(x) having integer coefficients.
(ii) Sketch the graph of y=p(x) on a suitable scale, clearly marking all intercepts with the coordinate axes.
(iii) From your sketch, state whether the leading coefficient of p(x) is positive or negative and explain your answer in one or two sentences.