Consider the polynomial f(x)=x4−5x3+2x2+20x−24.
(i) Using the appropriate test, verify whether x−2 is a factor of f(x).
(ii) Verify in the same manner whether x+3 is a factor of f(x).
(iii) Using any factor found in parts (i) or (ii), factorise f(x) completely.
(iv) Hence list all real zeros of f(x).