Đáp án:
Giải thích các bước giải:
a, `x^3-2x-1`
`=x^3+x^2-x^2-x-x-1`
`=(x^3+x^2)-(x^2+x)-(x+1)`
`=x^2(x+1)-x(x+1)-(x+1)`
`=(x+1)(x^2-x-1)`
b, `2x^4-3x-5`
`=2x^4+2x^3−2x^3−2x^2+2x^2+2x−5x−5`
`=2x^3(x+1)-2x^2(x+1)+2x(x+1)−5(x+1)`
`=(x+1)(2x^3-2x^2+2x−5)`
c, `x^3-2x-4`
`=x^3−2x^2+2x^2−4x+2x−4`
`=x^2(x-2)+2x(x-2)+2(x-2)`
`=(x-2)(x^2+2x+2)`
d, `x^4+x^3+2x-4`
`=x^4−x^3+2x^3−2x^2+2x^2−2x+4x−4`
`=x^3(x-1)+2x^2(x-1)+2x(x-1)+4(x-1)`
`=(x-1)(x^3+2x^2+2x+4)`
`=(x-1)[x^2(x+2)+2(x+2)]`
`=(x-1)(x+2)(x^2+2)`
e, `x^7-6x+5`
`=x^7−x^6+x^6−x^5+x^5−x^4+x^4−x^3+x^3−x^2+x^2−x−5x+5`
`=x^6(x-1)+x^5(x-1)+x^4(x-1)+x^3(x-1)+x^2(x-1)+x(x-1)−5(x-1)`
`=(x-1)(x^6+x^5+x^4+x^3+x^2+x−5)`
f, `x^5+x-2`
`=x^5−x^4+x^4−x^3+x^3−x^2+x^2−x+2x−2`
`=x^4(x-1)+x^3(x-1)+x^2(x-1)+x(x-1)+2(x-1)`
`=(x-1)(x^4+x^3+x^2+x+2)`
