If the polynomial x¹⁹ + x^{17 ​}​ + x¹³ + x¹¹ + x⁷ + x⁵ + x³ is divided by x² + 1, find the remainder.
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Dear Student,

Please find below the solution to the asked query:

We find value of $\frac{x^{19} + x^{17} + x^{13} + x^{11} + x^7 + x^5 + x^3}{x^2 + 1}$ by long division method , As :


So, We write remainder :  x¹⁷  + x¹³  + x⁷ + x  - $\frac{\mathbf{x}}{{\mathbf{x}}^{\mathbf{2}}\mathbf{ }\mathbf{+}\mathbf{ }\mathbf{1}}$


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