`a)12x^3+4x^2-27x-9`
`=(12x^3+4x^2)-(27x+9)`
`=4x^2(3x+1)-9(3x+1)`
`=(3x+1)(4x^2-9)`
`=(3x+1)(2x-3)(2x+3)`
`b)x^4-25x^2+20x-4`
`=x^4+5x^3-5x^3-2x^2-25x^2+2x^2+10x+10x-4`
`=(x^4+5x^3-2x^2)-(5x^3+25x^2-10x)+(2x^2+10x-4)`
`=x^2(x^2+5x-2)-5x(x^2+5-2)+2(x^2+5x-2)`
`=(x^2-5x+2)(x^2+5x-2)`
`c)x^2(x^2-6)-x^2+9`
`=x^4-6x^2-x^2+9`
`=(x^4-6x^2+9)-x^2`
`=(x^2-3)^2-x^2`
`=(x^2-3-x)(x^2-3+x)`