x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
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x3 - 2x2 - 4x + 8 = (x2 - 4)(x - 2) = (x + 2)(x - 2)(x - 2)
3 - 3x + x2 - x3 = (1 - x)(x2 + 3)
x3 - 4x = x(x2 - 4) = x(x + 2)(x - 2)
Dividend: 4x4-x3+17x2+11x+4 Divisor: 4x+3 Quotient: x3-x2+5x-1 Remainder: 7
(x + 4) / (x3 - 11x + 20) = (x + 4) / (x2 + 4x - 5)(x + 4) = 1 / (x2 + 4x - 5) = 1 / (x + 5)(x - 1), where x ≠ -4