Đáp án:
$a) (x -3).(x +2).(x +4)$
$b) (x -4).(x -2).(2x +1)$
$c) (x -6).(x -2).(x -1).(x +1)$
$d) (x -3).(x -2).(x +1).(-3x +8)$
Giải thích các bước giải:
$a)$ `x^3 +3x^2 -10x -24 `
`= x^2.(x -3) +6x.(x -3) +8.(x -3)`
`= (x -3).(x² +6x +8)`
`= (x -3).[x.(x +2) +4.(x +2)]`
`= (x -3).(x +2).(x +4)`
$b)$ `2x^3 -11x^2 +10x +8`
`= 2x².(x -4) -3x.(x -4) -2.(x -4)`
`= (x -4).(2x² -3x -2)`
`= (x -4).[2x.(x -2) +(x -2)]`
`= (x -4).(x -2).(2x +1)`
$c)$ `x^4 -8x^3 +11x^2 +8x -12`
`= x³.(x -6) -2x².(x -6) -x.(x -6) +2.(x -6)`
`= (x -6).(x³ -2x² -x +2)`
`= (x -6).[x².(x -2) -(x -2)]`
`= (x -6).(x -2).(x² -1)`
`= (x -6).(x -2).(x -1).(x +1)`
$d)$ `-3x^4 +20x^3 -35x^2 -10x +48`
`= -3x³.(x -3) +11x².(x -3) -2x.(x -3) -16.(x -3)`
`= (x -3).(-3x³ +11x² -2x -16)`
`= (x -3).[-3x².(x -2) +5x.(x -2) +8.(x -2)]`
`= (x -3).(x -2).(-3x² +5x +8)`
`= (x -3).(x -2).[-3x.(x +1) +8.(x +1)]`
`= (x -3).(x -2).(x +1).(-3x +8)`
