因式分解 高手来 追分

来源：百度知道 编辑：UC知道 时间：2024/06/23 01:14:27
1 （X^2+X+1)(X^2+X+2）-12
2 bc^2+a^2c+ab^2-a^2b-b^2c-c^2a
3 X^3+4X^2-5
4 X^3+X+30
5 (X+1）（X+3）（X+5）（X+7）+15
6 X（X+1）（X+2）（X+3）-24

1 （X^2+X+1)(X^2+X+2）-12
=(x^2+x+1)^2+(x^2+x+1)-12
=(x^2+x+1+4)(x^2+x+1-3)
=(x^2+x+5)(x^2+x-2)
=(x^2+x+5)(x-1)(x+2)

2 bc^2+a^2c+ab^2-a^2b-b^2c-c^2a
=(bc^2-b^2c)+(a^2c-a^2b)+(ab^2-ac^2)
=bc(c-b)+a^2(c-b)+a(b^2-c^2)
=bc(c-b)+a^2(c-b)-a(b+c)(c-b)
=(c-b)(bc+a^2-ab-ac)
=(c-b)[b(c-a)+a(a-c)]
=(c-b)(c-a)(a-b)

3 X^3+4X^2-5
=x^3-1+4x^2-4
=(x^3-1)+4(x^2-1)
=(x-1)(x^2+x+1)+4(x+1)(x-1)
=(x-1)(x^2+x+1+4x+4)
=(x-1)(x^2+5x+5)

4 X^3+X+30
=x^3+3x^2-3x^2+x+30
=x^2(x+3)-(3x^2-x-30)
=x^2(x+3)-(x+3)(3x-10)
=(x+3)(x^2-3x+10)

5 (X+1）（X+3）（X+5）（X+7）+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x+7)^2+8(x^2+8x+7)+15
=(x^2+8x+7+3)(x^2+8x+7+5)
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)

6 X（X+1）（X+2）（X+3）-24
=[x(x+3)][(x+1)(x+2)]-24
=(x^2+3x)(x^2+3x+2)-24
=(x^2+3x)^+2(x^2+