Let p(x)=x3+ax2+bx+c, where a, b and c are real numbers.
a. (i) Show that the remainder obtained when p(x) is divided by x−1 is 1+a+b+c.
b. (ii) Hence prove that x−1 is a factor of p(x) if and only if a+b+c=−1.
c. (iii) If a=2 and b=−3, determine the value of c for which x−1 is a factor of p(x).