Using the long divison method, the remainder when x⁴ + 36 is divided by x² - 8 is 100
_____x²+8
___________
x² - 8 | x⁴ + 36
____ | x⁴ - 8x²
-________8x² + 36
-________8x² - 64
___________100
The remainder is calculated as (36 - (-64)) = (36 + 64) = 100
Therefore, the remainder is 100
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