Question

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81x ^4 + 9x ^2 + 1
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9x ^2 +3x + 1

Answer 1

$\dfrac{81x^4+9x^2+1}{9x^2+3x+1}=\dfrac{81x^4+18x^2+1-9x^2}{9x^2+3x+1}=\dfrac{(9x^2+1)^2-9x^2}{9x^2+3x+1}=\\ \\ \\ =\dfrac{(9x^2-3x+1)(9x^2+3x+1)}{9x^2+3x+1}=9x^2-3x+1$