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

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To divide the polynomial x^3 + (1-k^2)x + k by (x+k) using synthetic division, the process involves setting up the synthetic division with -k as the divisor. The resulting synthetic division yields coefficients that simplify to x^2 - kx + 1. This shows that the polynomial can be expressed as x^3 + (1-k^2)x + k = (x+k)(x^2 - kx + 1). The method effectively demonstrates how to perform synthetic division with a linear binomial. Understanding this technique is crucial for polynomial division in algebra.
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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