`24x^5+10x^4-x^3-19x^2-5x+6`
`=24x^5-12x^4+22x^4-11x^3+10x^3-5x^2-14x^2+7x-12x+6`
`=(24x^5-12x^4)+(22x^4-11x^3)+(10x^3-5x^2)-(14x^2-7x)-(12x-6)`
`=12x^4(2x-1)+11x^3(2x-1)+5x^2(2x-1)-7x(2x-1)-6(2x-1)`
`=(12x^4+11x^3+5x^2-7x-6)(2x-1)`
`=(12x^4+8x^3+3x^3+2x^2+3x^2+2x-9x-6)(2x-1)`
`=[(12x^4+8x^3)+(3x^3+2x^2)+(3x^2+2x)-(9x+6)](2x-1)`
`=[4x^3(3x+2)+x^2(3x+2)+x(3x+2)-3(3x+2)](2x-1)`
`=(4x^3+x^2+x-3)(3x+2)(2x-1)`
`=(4x^3-3x^2+4x^2-3x+4x-3)(3x+2)(2x-1)`
`=[(4x^3-3x^2)+(4x^2-3x)+(4x-3)](3x+2)(2x-1)`
`=[x^2(4x-3)+x(4x-3)+(4x-3)](3x+2)(2x-1)`
`=(x^2+x+1)(4x-3)(3x+2)(2x-1).`
