`a)4x²-6x`
`=2x.2x-2x.3`
`=2x(2x-3)`
`b)x³y-2x²y²+5xy`
`=xy.x²-xy.2xy+xy.5`
`=xy(x²-2xy+5)`
`c)2(x-1)³-5(x-1)²-(x-1)`
`=(x-1)[2(x-1)²-5(x-1)-1]`
`=(x-1)[2(x²-2x+1)-5x+5-1]`
`=(x-1)(2x²-4x+2-5x+5-1)`
`=(x-1)(2x²-9x+6)`
`d)x(y-x)³-y(x-y)²+xy(x-y)`
`=x(y-x)³-y(y-x)²-xy(y-x)`
`=(y-x)[x(y-x)²-y(y-x)-xy]`
`=(y-x)[x(y²-2xy+x²)-y²+xy-xy]`
`=(y-x)(xy²-2x²y+x³-y²+xy-xy)`
`=(y-x)(xy²-2x²y+x³-y²)`
`e)2x²(x+1)+4x(x+1)`
`=(x+1)(2x²+4x)`
`=2x(x+1)(x+2)`