Originally Posted by

**Quacky** I have a few questions about algebraic division:

a)As an example, how would I work out $\displaystyle 2x^3-4x^2+6x-3$ divided by $\displaystyle x+1$?

I've never understood algebraic long division so a step by step guide (or link) would be greatly appreciated.

b) If I have something like $\displaystyle 2x^3-4x^2+6x-3$ divided by $\displaystyle 2x+1$, how would I use the remainder theorem to work out the remainder? would I substiture in x=-0.5?

Thanks in advance.

To a) You use the first summand of the divisor as divisor. To find the term which has to be subtracted you use the complete divisor. (Please read this sentence three times before you decide that you didn't understand it )

Code:

(2x^2 - 4x^2 + 6x - 3) ÷ (x + 1) = 2x^2 - 6x + 12, R = -15
-(2x^3 + 2x^2)
---------------
-6x^2 + 6x
-(-6x^2 - 6x)
-------------
12x - 3
-(12x + 12)
-----------------
-15

to b) Yes.