Question 1028752
your equation is x^3 - 2x^2 + px6.


i re-wrote it as x^3 - 2x^2 + 6px.


this is because x is the variable, therefore 6 and p must be the constants.


i used synthetic division by dividing 2 into (1 - 2 + 6p + 0) and got a remainder of 12p.


i then used regular polynomial division and got a remainder of 12p.


i then said that f(x) = x^3 - 2x^2 + 6px and then solved for f(2).


i got f(2) = 2^3 - 2*2^2 + 6*p*2 which resulted in 8 - 8 + 12*p which resulted in 12p.


looks to me like the remainder is 12p.


that's your remainder in terms of p.


i'm not quite sure where you got 2p-6 from.