a) $A = x^3 - x^2 + x -1$
$= x^2(x -1) + (x -1)$
$= (x -1)(x^2 +1)$
b) $B = x^3 - 3x^2 + 4x - 12$
$= x^2(x - 3) + 4(x -3)$
$=(x -3)(x^2 + 4)$
c) $C = x^3 - 5x^2 + 10x - 8$
$= (x^3 - 8) - (5x^2 - 10x)$
$= (x -2)(x^2 + 2x + 4) - 5x(x - 2)$
$= (x -2)(x^2 - 3x + 4)$
d) $D = x^2 - 4xy - 16 + 4y^2$
$= (x^2 - 4xy + 4y^2) - 4^2$
$= (x - 2y)^2 - 4^2$
$= (x - 2y - 4)(x - 2y + 4)$
