$a)_{}$ $x^6-2x^3+2x^5+1-2x^2_{}$
$=(x^6-2x^3+1)+(2x^5-2x^2)_{}$
$=(x^3-1)+2x^2.(x^3-1)_{}$
$=(x^3-1)(x^3+2x^2-1)_{}$
$=(x^3-1)(x^3+x^2+x^2-1)_{}$
$=(x-1)(x^2+x+1)(x+1)(x^2+x-1)_{}$
$b)_{}$ $x^3-x-6_{}$
$=x^3-2^3-x+2_{}$
$=(x^3-2^3)-(x-2)_{}$
$=(x-2)(x^2+2x+4)-(x-2).1_{}$
$=(x-2)(x^2+2x+3)_{}$
$c)_{}$ $x^3-6x^2+9x_{}$
$=x.(x^2-6x+9)_{}$
$=x.(x-3)^2_{}$