`a)x^3-9x^2+6x+16`
`=x^3+x^2-2x^2-2x-8x^2-8x+16x+16`
`=x^2(x+1)-2x(x+1)-8x(x+1)+16(x+1)`
`=(x^2-2x-8x+16)(x+1)`
`=[x(x-2)-8(x-2)](x+1)`
`=(x-8)(x-2)(x+1)`
`b)x^3-x^2-x-2`
`=x^3+x^2+x-2x^2-2x-2`
`=x(x^2+x+1)-2(x^2+x+1)`
`=(x-2)(x^2+x+1)`
`c)x^3+x^2-x+2`
`=x^3-x^2+x+2x^2-2x+1`
`=x(x^2-x+1)+2(x^2-x+1)`
`=(x+2)(x^2-x+1)`
`d)x^3-6x^2-x+30`
`=x^3+2x^2-3x^2-6x-5x^2-10x+15x+30`
`=x^2(x+2)-3x(x+2)-5x(x+2)+15(x+2)`
`=(x^2-3x-5x+15)(x+2)`
`=[x(x-3)-5(x-3)](x+2)`
`=(x-5)(x-3)(x+2)`
`e)x^3-7x-6`
`=x^3+2x^2-3x^2-6x+x^2+2x-3x-6`
`=x^2(x+2)-3x(x+2)+x(x+2)-3(x+2)`
`=(x^2-3x+x-3)(x+2)`
`=[x(x-3)+(x-3)](x+2)`
`=(x-3)(x+1)(x+2)`
