The remainder is 8.
(x2 + 4)/(x - 2) = (x + 2) + 8/(x - 2)
or
x2 + 4 = (x - 2)(x + 2) + 8
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(3x4 + 2x3 - x2 - x - 6)/(x2 + 1)= 3x2 + 2x - 4 + (-3x - 2)/(x2 + 1)= 3x2 + 2x - 4 - (3x + 2)/(x2 + 1)where the quotient is 3x2 + 2x - 4 and the remainder is -(3x + 2).
Dividend: 4x4-x3+17x2+11x+4 Divisor: 4x+3 Quotient: x3-x2+5x-1 Remainder: 7
7.8
749 ÷ 4 = 187 remainder 1
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)