Polynomials Test

1. Complete the following statement about the factor theorem:

If f(b) = 0, ……………………………………..                                                                                         [1]

2a) The remainder when the expression x³ – 11x² + kx – 30 is divided by x – 1 is 4 times the remainder when this expression is divided by x – 2. Find the value of the constant k.                                                               [4]

b) Solve the equation x³ – 4x² – 8x + 8 = 0, expressing non-integer solutions in the form a ± √b, where a and b are integers.                                                                                                                               w07p1q8 [5]