When a polynomial $p(x)$ of degree 3 is divided by $3x^2 − 8x + 5$, quotient and remainder obtained are linear polynomials such that $p(1)$ = 19 and $p(5/3)$ = 25. So, find the remainder polynomial.
Please give thorough explanation. I tend to be slow at picking up new things. ;) I'm in 10th grade, so if you use any concept which is above the level of an average 10th grade student, please explain it.
I'll be really grateful.