When a polynomial P(x) is divided by x+1, x+2, and x+3, the remainders are 2, 3, and 6 respectively. Find the remainder when P(x) is divided by (x+1)(x+2)(x+3).

I need someone to help me with this problem, since I forgot how to start them off.

Expand P(x)

Ax^n + Bx^n-1 .... ax^2 + bx + c

perform the division for the trinomial (P(x) may be a higher order but it doesn't matter)

you'll get 3 equations with three variables. Solve for a, b, c.

then divide it out.

Do you still need help on the problem? I think there is something wrong with it, because if you treat P(x) as a trinomial rather than a binomial you have an unsolvable set of equations that should also lead to the correct answer, but can't.

anyway its been years since Algebra 2 and I am going off on this with just basic math knowledge