Additional Maths Factor and Remainder Theorem

1.  State the remainder theorem:                                                                                       [1]

2.   Solve for p, q and r: 3x² + 6x – 4 ≡ p(x –q) ² + r                                                         [3]

3.  The polynomial P(x) = x³ + ax² + bx – 3 has a remainder of 27 when divided by    x – 2, and a remainder of 3 when divided by x + 1.   Calculate the remainder when P(x) is divided by x – 1.                                                                                                  [4]

4. Is 2x – 3 a factor of  3x³ + 2x²  – 7x + 2?                                                                      [2]

5.  Solve the equation 2x³ + 3x² – 32x + 15 = 0.                                                              [6]