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Đáp án+Giải thích các bước giải:
`6)`
`x^{2}+2x-15`
`=x^{2}+5x-3x-15`
`=x.(x+5)-3.(x+5)`
`=(x-3).(x+5)`
`7)`
`x^{3}x+3x^{2}y+3xy^{2}-y+y^{3}`
`=>` Đề có vẻ bị lỗi và thiếu dấu,dữ kiện
`8)`
`x^{3}-3x^{2}-4x+12`
`=x^{2}.(x-3)-4.(x-3)`
`=(x-3).(x^{2}-2^{2})`
`=(x-3).(x-2).(x+2)`
`9)`
`x^{2}-7xy+10y^{2}`
`=x^{2}-2xy-5xy+10y^{2}`
`=x.(x-2y)-5y.(x-2y)`
`=(x-5y).(x-2y)`
`10)`
`a^{4}+4`
`=a^{4}+4a^{2}+4-4a^{2}`
`=(a^{2})^{2}+2.a^{2}.2+2^{2}-4a^{2}`
`=(a^{2}+2)^{2}-(2a)^{2}`
`=(a^{2}-2a+2).(a^{2}+2a+2)`
`11)`
`2x^{3}+3x^{2}-5x`
`=x.2x^{2}+x.3x-x.5`
`=x.(2x^{2}+3x-5)`
`=x.(2x^{2}+5x-2x-5)`
`=x.[x.(2x+5)-1.(2x+5)]`
`=x.(x-1).(2x+5)`
`12)`
`(x+y+z)^{3}-x^{3}-y^{3}-z^{3}`
`=[(x+y+z)^{3}-x^{3}]-(y^{3}+z^{3})`
`=(x+y+z-x).[(x+y+z)^{2}+(x+y+z).x+x^{2}]-(y+z).(y^{2}-yz+z^{2})`
`=(y+z).[(x+y)^{2}+2.(x+y).z+z^{2}+x^{2}+xy+xz+x^{2}]-(y+z)(y^{2}-yz+z^{2})`
`=(y+z).(x^{2}+2xy+y^{2}+2xz+2yz+z^{2}+x^{2}+xy+xz+x^{2}-y^{2}+yz-z^{2})`
`=(y+z).(3x^{2}+3xy+3yz+3xz)`
`=3.(y+z).(x^{2}+xy+yz+xz)`
`=3.(y+z).[x.(x+y)+z.(x+y)]`
`=3.(y+z).(x+z).(x+y)`
`13)`
`2x^{3}-4x^{2}+2x-4`
`=2x^{2}.(x-2)+2.(x-2)`
`=(x-2).(2x^{2}+2)`
`=2.(x-2).(x^{2}+1)`
`14)`
`x^{3}-4x^{2}-8x+8`
`=x^{3}-6x^{2}+2x^{2}+4x-12x+8`
`=x^{2}.(x+2)-6x(x+2)+4.(x+2)`
`=(x+2).(x^{2}-6x+4)`
`15)`
`3x^{5}-10x^{4}-8x^{3}-3x^{2}+10x+8`
`=3x^{5}-12x^{4}+2x^{4}-8x^{3}-3x^{2}+12x-2x+8`
`=(3x^{5}+2x^{4}-3x^{2}-2x)-(12x^{4}+8x^{3}-12x-8)`
`=x.(3x^{4}+2x^{3}-3x-2)-4.(3x^{4}+2x^{3}-3x-2)`
`=(x-4).(3x^{4}+5x^{3}-3x^{3}-5x^{2}+5x^{2}-5x+2x-2)`
`=(x-4).[3x^{3}.(x-1)+5x^{2}.(x-1)+5x.(x-1)+2.(x-1)]`
`=(x-4).(x-1).(3x^{3}+5x^{2}+5x+2)`
`=(x-4).(x-1).(3x^{3}+3x^{2}+2x^{2}+2x+3x+2)`
`=(x-4).(x-1).[x^{2}.(3x+2)+x.(3x+2)+1.(3x+2)]`
`=(x-4).(x-1).(3x+2).(x^{2}+x+1)`
`16)`
`x^{2}+2xy-9y^{2}+2xz+14yz-3z^{2}`
`=(x^{2}+2xy+y^{2}+2xz+2yz+z^{2})+12yz-4z^{2}-10y^{2}`
`=[(x+y)^{2}+2.(x+y).z+z^{2}]+(-10y^{2}+12yz-4z^{2})`
`=(x+y+z)^{2}+(-9y^{2}-y^{2}+12yz+2xz-4z^{2})`
`=(x+y+z)^{2}+[-(9y^{2}-12yz+4z^{2}))-y^{2}]`
`=(x+y+z)^{2}-{[(3y)^{2}-2.3y.2z+(2z)^{2}]+y^{2}}`
`=(x+y+z)^{2}-(3y-2z)^{2}-y^{2}`
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