I prefer using the "comparing coefficients" method (I think that's what it's called. It's not actually in my textbook.) because I'm completely hopeless at the other methods.
This is the method I mean. It's just an example. (x^3 + 4x^2 + x -6)/(x - 2) = Ax^2 + Bx + C
And multiply both sides by the divisor and just go through the letters A, B and C to find out the value.
But what do I do when there's a remainder? How would I finish this question?
(x^3 + 3x^2 + 6x + 1)/(x + 1)
I make (x^3 + 3x^2 + 6x + 1) = (Ax^2 + Bx + C)(x + 1)
coefficient of x^3 : 1 = A therefore A = 1
coefficient of x^2 : 3 = A + B therefore B = 2
coefficient of x^1 : 6 = B + C therefore C = 4
coefficient of x^0 : 1 = C therefore C = 1
Obviously my last value of C is wrong. How do I work out the remainder please? Rep on offer. Thanks.