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Our final remainder is 1.
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Here's a sample of how to find one of the solutions to our cubic equation with synthetic division: -1 | 2 9 13 6 __| -2-7-6 __| 2 7 6 0 Since we got a final remainder of 0, we know that one of our cubic's integer solutions is -1.
Write the final remainder on the division bar.
One last subtraction problem to find the final remainder, then we'll be done.
Since the determinant of M is never zero, the vector of the final remainders can be solved using the inverse of M : \begin{pmatrix} g \\ 0 \end{pmatrix} = \mathbf{M}^{-1} \begin{pmatrix} a \\ b \end{pmatrix} = (-1)^{N+1} \begin{pmatrix} m_{22} & -m_{12} \\ -m_{21} & m_{11} \end{pmatrix} \begin{pmatrix} a \\ b \end{pmatrix} \,.
In our example, our remainder is 2. Putting this over our original denominator (5), we get 2/5.
In the remainder of this paper, we show preliminary findings and methods that helped us reach our final conclusions, including how we arrived at an adequate number of singular values that allowed us to separate a set of species into groups with biological significance.
Note that, in the event that 10 didn't divide evenly into our final number, we'd need to account for the amount of 10 that is left over - the remainder.
Our final picks?
* Our final amnesiac is Nadine Dorries.
This is our final column.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com