A polynomial p(x)=3x3−4x2+7x−2 is given.
(i) State the Remainder Theorem.
(ii) Find the remainder when p(x) is divided by (x−3).
(iii) Verify your answer to part (ii) by direct substitution in p(x).
(iv) Is (x−3) a factor of p(x)? Give a reason for your answer.