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The first polynomial is not a factor of second polynomial
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Given : x^2 + 1, x^4 - 3x^3 - 4x^2 + 3x + 2.
x^2 + 1) x^4 - 3x^3 - 4x^2 + 3x + 2 ( x^2 - 3x - 5
x^4 + x^2
-------------------------------------
-3x^3 - 5x^2 + 3x + 2
- 3x^3 - 3x
---------------------------------------
-5x^2 + 6x + 2
-5x^2 - 5
--------------------------------------
6x + 7
Quotient = x^2 - 3x - 5, Remainder = 6x + 7.
Since, the remainder is not 0.
Therefore, x^2 + 1 is not a factor of x^4 - 3x^3 - 4x^2 + 3x + 2.
Hope it helps!
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