`a)x^2-x-12`
`=x^2-4x+3x-12`
`=x(x-4)+3(x-4)`
`=(x-4)(x+3)`
`b)x^2-5x-24`
`=x^2-8x+3x-24`
`=x(x-8)+3(x-8)`
`=(x-8)(x+3)`
`c)3x^2+13x-10`
`=3x^2+15x-2x-10`
`=3x(x+5)-2(x+5)`
`=(x+5)(3x-2)`
`d)x^4+2x^2-3`
`=x^4-x^2+3x^2-3`
`=x^2(x^2-1)+3(x^2-1)`
`=(x^2-1)(x^2+3)`
`=(x-1)(x+1)(x^2+3)`
`e)4x^4+81`
`=4x^4+2.2x^2*9+81-36x^2`
`=(2x^2+9)^2-(6x)^2`
`=(2x^2-6x+9)(2x^2+6x+9)`
`f)64x^4+y^4`
`=(8x^2)^2+2.(8x^2).y^2+y^4-16x^2y^2`
`=(8x^2+y^2)^2-(4xy)^2`
`=(8x^2-4xy+y^2)(8x^2+4xy+y^2)`
`g)x^4+324`
`=x^4+2.x^2*18+(18)^2-36x^2`
`=(x^2+18)^2-(6x)^2`
`=(x^2-6x+18)(x^2+6x+18)`
`h)(x^2-3)^2+16`
`=x^4-6x^2+9+16`
`=x^4-6x^2+25`
`=x^4+10x^2+25-16x^2`
`=(x^2+5)^2-(4x)^2`
`=(x^2-4x+5)(x^2+4x+5)`.