right, I understand when i get a question like x^3 + 2x^2+4x +3 divide that by (x+3) i get a quotient multiplied by divisor + a remainder.
This puts it into form like (AX^2+BX+C)(X+3) +D
I then solve it to find a b, c, d. I can solve this fine.
However, depending on the question the form of the quotient and the remaindeer will be different, e..g the remainder might be CX + D, etc.
How can I tell what form it will be in?
a rough method I just made up was look at the original expression and look at the divisor, if the divisor is (x-2) and the expression is x^3+3x^2-6x-3. I know that my quotient will only have things in it, which when multipled by the x from the x-2 make the original expression. e.g. the quotient will be (Ax^2+Bx-C) as I know that if i multipy everything by x I get basically the orioginal experession back except for the -3 which I treat as the remainder and thereofr just D.
Does that make sense as a method, is it ok?