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
x3 - 2x2 - 4x + 8 = (x2 - 4)(x - 2) = (x + 2)(x - 2)(x - 2)
x3 + 6x2 - 4x - 24 = (x + 6)(x2 - 4) = (x + 6)(x + 2)(x - 2)
64 is the cube of 4 so: x3 + 64 = (x + 4)(x2 - 4x + 16)
x3 + 3x2 - 4x -12 x2(x + 3) - 4(x + 3) (x2 - 4)(x+3)
x(x + 4)(x - 4) or x3 - 16x
x2(x3 + 1) is the best you can do there.
3 - 3x + x2 - x3 = (1 - x)(x2 + 3)
x3 + x2 - 3x - 3 x(x2 + x - 3) - 3
3x3 + 192 = 3*(x3 + 64) = 3*(x + 4)*(x2 - 4x + 16)
x3 - 4x = x(x2 - 4) = x(x + 2)(x - 2)
x3+27y3 = (x+3y) · (x2-3xy+9y2)
X3 - 4X2 - 45XX(X2 - 4X - 45)=============X is only common factor here.