Hướng dẫn trả lời:
a) `x^4 + x^3 - x^2 - 1.`
`= x^4 + 2x^3 + x^2 + x - x^3 - 2x^2 - x - 1.`
`= (x^4 + 2x^3 + x^2 + x) - (x^3 + 2x^2 + x + 1).`
`= x.(x^3 + 2x^2 + x + 1) - (x^3 + 2x^2 + x + 1).`
`= (x - 1).(x^3 + 2x^2 + x + 1).`
b) `x^4 - 3x^3 - x + 3.`
`= (x^4 - x) - (3x^3 - 3).`
`= x.(x^3 - 1) - 3.(x^3 - 1).`
`= (x - 3).(x^3 - 1).`
`= (x - 3).(x - 1).(x^2 + x + 1).`
c) `3x + 3y - x^2 - 2xy - y^2.`
`= (3x + 3y) - (x^2 + 2xy + y^2).`
`= 3.(x + y) - (x + y)^2.`
`= (x + y).[3 - (x + y)].`
`= (x + y).(3 - x - y).`
d) `2x - 2y - x^2 + 2xy - y^2.`
`= (2x - 2y) - (x^2 - 2xy + y^2).`
`= 2.(x - y) - (x - y)^2.`
`= (x - y).[2 - (x - y)].`
`= (x - y).(2 - x + y).`
`= - (x - y).(x - y - 2).`
e) `x^2y - y^3 - 2y^2 - y.`
`= y.(x^2 - y^2 - 2y - 1).`
`= y.[x^2 - (y^2 + 2y + 1)].`
`= y.[x^2 - (y + 1)^2].`
`= y.[x + (y + 1)].[x - (y + 1)].`
`= y.(x + y + 1).(x - y - 1).`
f) `x^3z + 2x^2yz + xy^2z - 9xz.`
`= xz.(x^2 + 2xy + y^2 - 9).`
`= xz.[(x^2 + 2xy + y^2) - 9].`
`= xz.[(x + y)^2 - 3^2].`
`= xz.[(x + y) + 3].[(x + y) - 3].`
`= xz.(x + y + 3).(x + y - 3).`
