# polynomial division

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• Mar 9th 2010, 03:14 PM
Jones
polynomial division
Hi,

Im trying to get my head around how to do polynomial division with undetermined coefficients.

Im trying to divide $z^2-2z+2$
into $z^4-2z^3+az-8z+8$

I run into problems when trying to subtract $2z^2$ from $az^2$

help appreciated
• Mar 10th 2010, 12:25 AM
earboth
Quote:

Originally Posted by Jones
Hi,

Im trying to get my head around how to do polynomial division with undetermined coefficients.

Im trying to divide $z^2-2z+2$
into $z^4-2z^3+az-8z+8$

I run into problems when trying to subtract $2z^2$ from $az^2$

help appreciated

According to your explanations I assume that the quotient reads:

$(z^4-2z^3+az^{\bold{\color{red}2}}-8z+8) \div (z^1-2z+2)$

Use long division:
Code:

```                                              (z-1)(2a-12)   z^4-2z^3+az^2-8z+8)÷(z^1-2z+2) = z^2+(a-2) + -----------                                                 z^2-2z+2 -(z^4-2z^3+2z^2) ------------------           (a-2)z^2-8z+8         -((a-2)z^2-2(a-2)z+2(a-2)         --------------------------                   -12z+2az-2a+12```
The remainder can be factored as shown in the final result.
• Mar 10th 2010, 01:37 AM
HallsofIvy
And, specifically, subtracting $2z^2$ from $az^2$ gives $az^2- 2z^2= (a- 2)z^2$