Phân tích thành nhân tử:
a) $x^{3}$-10$x^{}$-3
b) $x^{3}$- 3$x^{2}$+9$x^{}$-14
c) $x^{3}$-3$x^{2}$-$x^{}$-45
d) $x^{3}$-3$x^{2}$-4$x^{2}$+12
e) $x^{2}$-19$x^{}$-30
f) $x^{7}$+ $x^{5}$ +1
g) $x^{8}$+ $x^{7}$+1
h) $x^{5}$+ $x^{4}$+1
i) $x^{10}$+$x^{8}$+1
$a)_{}$ $x^3-10x-3_{}$
$⇔x^3+3x^2-3x^2-9x-x-3_{}$
$⇔x^2.(x+3)-3x.(x+3)-(x+3)_{}$
$⇔(x+3).(x^2-3x-1)_{}$
$b)_{}$ $x^3-3x^2+9x-14_{}$
$⇔x^3-2x^2-x^2+2x+7x-14_{}$
$⇔x^2.(x-2)-x.(x-2)+7.(x-2)_{}$
$⇔(x-2).(x^2-x+7)_{}$
$c)_{}$ $x^3-3x^2-x-45_{}$
$⇔x^3-5x^2+2x^2-10x+9x-45_{}$
$⇔x^2.(x-5)+2x.(x-5)+9.(x-5)_{}$
$⇔(x-5)(x^2+2x+9)_{}$
$d)_{}$ $x^3-3x^2-4x+12_{}$
$⇔x^2.(x-3)-4.(x-3)_{}$
$⇔(x-3)(x^2-4)_{}$
$⇔(x-2)(x+2)(x-3)_{}$
$e)_{}$ $x^3-19x-30_{}$
$⇔x^3+2x^2-2x^2-4x-15x-30_{}$
$⇔x^2.(x+2)-2x.(x+2)-15.(x+2)_{}$
$⇔(x+2)(x^2-2x-15)_{}$
$⇔(x+2)(x^2+3x-5x-15)_{}$
$⇔(x+2) .[x.(x+2)-5.(x+3) ] _{}$
$⇔(x+2)(x+3)(x-5)_{}$
$f)_{}$ $x^7+x^5+1_{}$
$⇔x^7+x^6-x^6+x^5-x^5+x^5-x^4+x^4+x^3-x^3+x^2-x^2-x+x+1_{}$
$⇔x^5.(x^2+x+1)-x^4.(x^2+x+1)+x^3.(x^2+x+1)-x.(x^2+x+1)+x^2+x+1_{}$
$⇔(x^2+x+1).(x^5-x^4+x^3-x+1)_{}$
$g)_{}$ $x^8+x^7+1_{}$
$⇔x^8+x^7+x^6-x^6-x^5-x^4+x^4+x^3-x^3+x^2-x^2+x-x+1_{}$
$⇔x^6.(x^2+x+1)-x^4.(x^2+x+1)+x^3.(x^2+x+1)-x.(x^2+x+1)+x^2+x+1_{}$
$⇔(x^2+x+1)(x^6-x^4+x^3-x+1)_{}$
$h)_{}$ $x^5+x^4+1_{}$
$⇔x^5+x^4+x^3-x^3-x^2+x^2-x+x+1_{}$
$⇔x^3.(x^2+x+1)-x.(x^2+x+1)+x^2+x+1_{}$
$⇔(x^2+x+1)(x^3-x+1)_{}$
$i)_{}$ tự làm nhé, tương tự nư trên rồi đặt nhân tử chung là đc, dài quá