Determining-product of a linear and cubic factor

Question

Question:

Product of a linear and cubic factor

(i) Determine the remainder when 9x⁵ - 4x⁴  is divided by 3x - 1

(ii) Show, using the factor theorem, that 2x -1  is a factor of 2x⁴ - x³ - 6x² +5x -1
   
and hence express 2x⁴ - x³ - 6x² + 5x -1 as a product of a linear and cubic factor.