SOLUTION: Question is as follows: Find in terms of p the remainder when x^3-2x^2+px6 is divided by x-2. I have done the P(x)=2, and subbed in to solve, and am left with 2p-6, and am not su

Question 1028752: Question is as follows:
Find in terms of p the remainder when x^3-2x^2+px6 is divided by x-2.
I have done the P(x)=2, and subbed in to solve, and am left with 2p-6, and am not sure how to go about the answer
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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