a)x3-4x2+8x-8
=x3-2x2+4x-2x2+4x-8
=x(x2-2x+4)-2(x2-2x+4)
=(x-2)(x2-2x+4)
b)x3-5x2-5x+1
=x3-6x2+x+x2-6x+1
=x(x2-6x+1)+(x2-6x+1)
=(x+1)(x2-6x+1)
c)x2y2-x2+8x-16
=x2y2+x2y-4xy-x2y-x2+4x+4xy+4x-16
=xy(xy+x-4)-x(xy+x-4)+4(xy+x-4)
=(xy-x+4)(xy+x-4)
d)x2-6xy+9y2+4x-12y
=9y2-3xy-12y-3xy+x2+4x
=3y(3y-x-4)-x(3y-x-4)
=(3y-x-4)(3y-x)
e)x2-xy+x3-3x2y+3xy2-y3
=x(x-y)+(x-y)3
=(x-y)[x+(x-y)2]
=(x-y)(x+x2-2xy+y2)
f)x4-x3+x2-1
=x4+x2+x-x3-x-1
=x(x3+x+1)-(x3+x+1)
=(x-1)(x3+x+1)
g)x4-x2+10x-25
=x4+x3-5x2-x3-x2+5x+5x2+5x-25
=x2(x2+x-5)-x(x2+x-5)+5(x2+x-5)
=(x2-x+5)(x2+x-5)
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