将下列各式因式分解 x^3-3x+2 　x^3-19x+30　x^3+6x^2+11x+6

因式分
x^3-3x+2 　
=x^3-x-2(x-1)
=x(x+1)(x-1)-2(x-1)
=(x-1)[x(x+1)-2]
=(x-1)(x^2+x-2)
=(x-1)(x+2)(x-1)
x^3-19x+30
=x^3-9x-10x+30
=x(x+3)(x-3)-10(x-3)
=(x-3)(x^2+3x-10)
=(x-3)(x+5)(x-2)
x^3+6x^2+11x+6
=x（x^2+6x+9）+2x+6
=（x+3）（x^2+3x+2）
=（x+3)（x+2)（x+1）

(1) x^3-3x+2 = x^3-x+2-2x= x^2（x-1）-2（x-1） =（x^2-2）（x-1）
(2) x^3-19x+30=x(x^2-9)-10(x-3)=x(x-3)(x+3)-10(x-3)=（x-3）（x^2+3x-10）
=(x-3)(x+5)(x-2)
(3) x^3+6x^2+11x+6=x（x^2+6x+9）+2x+6=（x+3）（2+x^2+3x）=（x+3）（x+2）（x+1）

“数学之美”团员448755083为你解答!x^3-3x+2=(x-2)(x-1)x^3-19x+30=(x^3-8)-19(x-2)=(x-2)(x^2+2x-15)x^3+6x^2+11x+6=(x^3-x)+6(x^2+2x+1)=x(x+1)(x-1)+6(x+1)^2=(x+1)(x^2-x+6x+6)=(x+1)(x^2+5x+6)=(x+1)(x+2)(x+3...

(1) x^3-3x+2
x^3-2x-x+2
=x^3-x-2x+2
=x(x^2-1)-2(x-1)
=x(x-1)(x+1)-2(x-1)
=(x-1)[x(x+1)-2]
=(x-1)(x^2+x-2)
=(x-1)(x+2)(x-1)
(2)x^3-19x+30
原式=x^3-9x-10x+30
=x(x^2-9)-10(x-3)
=x(x-3)(x+3)-10(x-3)
=(x-3)[x(x+3)-10]
=(x-3)(x^2+3x-10}
=(x-3)(x+5)(x-2)
(3)x^3+6x^2+11x+6=0
x=-1，左边=-1+6-11+6=0
右边=0
左边=右边
所以x=-1是原方程的根
x^3+6x^2+11x+6=(x+1)(ax^2+bx+c)=0(a/=0)
ax^3+bx^2+cx+ax^2+bx+c
=ax^3+(a+b)x^2+(b+c)x+c=x^3+6x^2+11x+6
a=1,a+b=6,b+c=11,c=6
b=5,c=6
(x+1)(x^2+5x+6)=(x+1)(x+2)(x+3)