How can I divide a polynomial by (x+k) using synthetic division?

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SUMMARY

The discussion focuses on dividing the polynomial \(x^3 + (1-k^2)x + k\) by \((x+k)\) using synthetic division. The synthetic division process is demonstrated with the coefficients of the polynomial and the divisor, resulting in the quotient \(x^2 - kx + 1\). The final expression confirms that \(x^3 + (1-k^2)x + k\) can be factored as \((x+k)(x^2 - kx + 1)\). This method effectively simplifies polynomial division for the given expression.

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markosheehan
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i am trying to divide x^3+(1-k^2)x+k by (x+k) but i can't do this can you show me how to.
 
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I would use synthetic division here:

$$\begin{array}{c|rr}& 1 & 0 & 1-k^2 & k \\ -k & & -k & k^2 & -k \\ \hline & 1 & -k & 1 & 0 \end{array}$$

Thus, we may state:

$$x^3+(1-k^2)x+k=(x+k)(x^2-kx+1)$$
 

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