Consider the function H(x)=x2−5x+6x3−6x2+11x−6.
a. (i) Factor the numerator and the denominator completely.
b. (ii) Hence determine all real numbers that are excluded from the domain of H(x).
c. (iii) Simplify H(x) to its lowest terms and classify the simplified expression as a polynomial function or a rational function.
d. (iv) Prove that H(x) is continuous at every real number except those excluded in part (ii).