Factorize-x3-x2-a x-x-a-1

We have: x3 x2+ax+x a 1=x3 x2+ax a+x 1 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; =x2x 1+ax 1+1 ...

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Factorize:x3-...

Question

Factorize:
x³ − x² + ax + x − a − 1

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Solution

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(x) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - a^{x} + x a^{x} {log}_{e} a}{a^{x} x^{2}}, x < 0 \frac{2^{x} a^{x} - x {log}_{e} 2 - x {log}_{e} a - 1}{x^{2}}, x < 0 \end{matrix}, a > 0

x = 0

(\frac{1 + x^{2} + x^{4}}{1 + x + x^{2}}) = a x + b

: (a, b) \equiv

\frac{x^{2} + 1}{x^{4} + x^{2} + 1} = \frac{A x + B}{x^{2} + x + 1} + \frac{C x + D}{x^{2} - x + 1} t h e n A - C =

x^{3} - x^{2} + a x - a + x - 1

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