Re: Polynomial Long Division

At each step, you borrow *a single* monomial from the dividend. You first write x^2 in the answer space, multiply x^2 by (x - 2) and subtract the result from *the first two monomials* of the dividend. This leaves -x^2. At this point, you borrow *a single monomial*: 12x and write -x^2 + 12x instead of -x + 12x - 5. Then you write -x in the answer space, multiply -x by (x - 2) and subtract the result from -x^2 + 12x. Only at this point you borrow the final monomial from the dividend: -5. Then you perform one more step.

Re: Polynomial Long Division

Hello, camorris!

Quote:

$\displaystyle \text{Show that: }\:\dfrac{x^3-3x^2+12x-5}{x-2} \;=\;(x^2-x+10) + \frac{15}{x-2}$

The division should look like this . . .

. . $\displaystyle \begin{array}{cccccccccc} &&&& x^2 & - & x &+& 10 \\ && -- & -- & -- & -- & -- & -- & -- \\ x-2 & ) & x^3 &-& 3x^2 &+& 12x &-&5 \\ && x^3 &-& 2x^2 \\ && --&--&-- \\ &&& -& x^2 &+& 12x \\ &&&-& x^2 &+& 2x \\ &&& --&--&--&-- \\ &&&&&& 10x &-& 5 \\ &&&&&&10x &-&20 \\ &&&&&& --&--&-- \\ &&&&&&&& 15 \end{array}$

Re: Polynomial Long Division

Thank you by the way I was nearly there although a couple of errors on my behalf ruined it