x3 - 2x2 - 4x + 8
= (x2 - 4)(x - 2)
= (x + 2)(x - 2)(x - 2)
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x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x3 - 2x2 + x - 2 =(x - 2)(x2 + 1)
x3 + 2x2 + 5x + 4 = (x + 1)(x2 + x + 4)
x3 + 2x2 - 19x - 20 = x3 + x2 + x2 + x - 20x - 20 = x2(x + 1) - x(x + 1) - 20(x + 1) = (x + 1)(x2 + x - 20) = (x + 1)(x - 4)(x + 5)
Dividend: 4x4-x3+17x2+11x+4 Divisor: 4x+3 Quotient: x3-x2+5x-1 Remainder: 7