Let g(x)=x4−5x3+6x2+x−3.
(a) Divide g(x) by x2−4x+3 and write down the quotient and the remainder.
(b) Hence express g(x) as a product of two quadratic (or linear) factors, if possible.
(c) Using the factorisation obtained in part (b), determine all the zeros of g(x).