# Method of detached coefficients division

drooble122
Homework Statement:
Divide 15+2m^4-31m+9m^2+4m^3+m^5 by 3-2m-m^2
Relevant Equations:
Use method of detached coefficients
-1 -2 3 | 1 2 4 9 -31 15 | -1 -7 5
1 2 -3
7 9 -31 15
7 14 -21
-5 -10 15
5 -10 15

The quotient has the coefficients -1, -7, 5. Now here is the problem. I assumed the variables would thus be -1m^2-7m-5. Turns out the correct answer is -1m^3-7m-5. But i thought in the quotient its all lined up from right to left by the power: 0,1,2,3...etc. Clearly this is not the case.
Any instruction on how to assign the proper power to the variable would be appreciated. Thanks.

Last edited:

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Homework Helper
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Homework Statement:: Divide 15+2m^4-31m+9m^2+4m^3+m^5 by 3-2m-m^2
Relevant Equations:: Use method of detached coefficients

-1 -2 3 | 1 2 4 9 -31 15 | -1 -7 5
1 2 -3
7 9 -31 15
7 14 -21
-5 -10 15
5 -10 15

The quotient has the coefficients -1, -7, 5. Now here is the problem. I assumed the variables would thus be -1m^2-7m-5. Turns out the correct answer is -1m^3-7m-5. But i thought in the quotient its all lined up from right to left by the power: 0,1,2,3...etc. Clearly this is not the case.
Any instruction on how to assign the proper power to the variable would be appreciated. Thanks.
You need zero as a place holder.
Line stuff up with "code".

Code:
   -1 -2 3 |       1 2  4  9  -31 15 | -1 0 -7 5
1 2 -3
______
0  7   9  -31 15
0  0   0
________
7   9  -31 15
7  14  -21
_________
-5  -10 15
-5  -10 15

jim mcnamara
Homework Helper
You need zero as a place holder.
Line stuff up with "code".

Code:
   -1 -2 3 |       1 2  4  9  -31 15 | -1 0 -7 5
1 2 -3
______
0  7   9  -31 15
0  0   0
________
7   9  -31 15
7  14  -21
_________
-5  -10 15
-5  -10 15
Thanks for this. Here I think this process is called 'synthetic division'. And I never understood it. Until now!

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