Answer the following questions about factors and remainders of polynomials.
(i) State the Factor Theorem for a polynomial in one variable.
(ii) Explain why, if the remainder obtained on dividing a polynomial p(x) by (x−a) is non-zero, the expression (x−a) cannot be a factor of p(x).
(iii) A polynomial f(x)=3x2+2x−1 is divided by (x+1) and the remainder is found to be −2. Verify this remainder by direct substitution and, using your answer to part (ii), comment on whether (x+1) is a factor of f(x).