[sharls]

I have no idea how to approach the following question:

The set P1 of all linear functions x 7→ ax + b is a two-dimensional linear space. A mapping A: P1 → P1 is defined by the rule: multiply a linear function ax + b by the linear function 4x + 6 and then take the remainder cx + b upon division of the resulting quadratic function by 6x 2 − x + 5. The remainder cx + b is the image of ax + b under A. The mapping A is a linear operator (one may wish to prove this as an exercise but this is not assessable). Find the matrix of the linear operator A in the basis 2x + 1, 2x + 4 of the linear space P1.