Polynomial that gives specific remainder

Question

How can I find a quintic polynomial which gives the remainder of 2x+3 when it's divided by x^2-4x+5? Can somebody explain me the process?

Answer 1

By definition of polynomial division $P(x)=(x^2-4x+5)(ax^3+bx+c)+2x+3$

and we need $a\ne 0$ so that the term in $x^5$ is not null, but except for this condition you can set any values for $a,b,c$.