You can use either the polynomial long division, or the polynomial remainder theorem. According to the latter, the remainder of f(x) divided by k(x-a) is f(a).1. Determine the remainder when 9x5 – 4x4 is divided by 3x-1

According to the polynomial remainder theorem above (in this case it is the same as the factor theorem), it is sufficient to represent 2x-1 as for some and and then to show that is the root of the given polynomial. To find the cubic factor, use the long division to divide the given fourth-degree polynomial by 2x - 1.2. Show, using 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