因式分解:x^3+6x^3+11x+6 6x^4+5x^3+3x^2-3x-2 x^4-11x^2+1 2x^3-ax^
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/25 18:35:54
因式分解:x^3+6x^3+11x+6 6x^4+5x^3+3x^2-3x-2 x^4-11x^2+1 2x^3-ax^2-5a^2x-2a^3
x^3+6x^2+11x+6
6x^4+5x^3+3x^2-3x-2
x^4-11x^2+1
2x^3-ax^2-5a^2x-2a^3
x^3+6x^2+11x+6
6x^4+5x^3+3x^2-3x-2
x^4-11x^2+1
2x^3-ax^2-5a^2x-2a^3
1.X^3+6X^2+11X+6
=(X^3+X^2)+(5X^2+5X)+(6X+6)
=X^2(X+1)+5X(X+1)+6(X+1)
=(X+1)(X^2+5X+6)
=(X+1)(X+2)(X+3)
2.6x^4+5x^3+3x^2-3x-2
=6x^4+5x^3+(x^2+2x^2)-3x-2
=(6x^4+5x^3+x^2)+(2x^2-3x-2)
=x^2(2x+1)(3x+1)+(2x+1)(x-2)
=(2x+1)(3x^3+x^2+x-2)
=(2x+1)(3x^3-3+x^2+x+1)
=(2x+1)[3(x-1)(x^2+x+1)+x^2+x+1]
=(2x+1)(3x-2)(x^2+x+1)
3.x^4-11x^2+1
=(x^4-2x^2+1)-9x^2
=(x^2-1)^2-(3x)^2
=(x^2+3x-1)(x^2-3x-1)
4.2x^3-ax^2-5a^2x-2a^3
=2x^3-ax^2-(2a^2x+3a^2x)-2a^3
=(2x^3-2a^2x)-(ax^2+3a^2x+2a^3)
=2x(x+a)(x-a)-a(x+a)(x+2a)
=(x+a)[2x(x-a)-a(x+2a)]
=(x+a)[2x^2-3ax-2a^2]
=(x+a)(x-2a)(2x+a)
=(X^3+X^2)+(5X^2+5X)+(6X+6)
=X^2(X+1)+5X(X+1)+6(X+1)
=(X+1)(X^2+5X+6)
=(X+1)(X+2)(X+3)
2.6x^4+5x^3+3x^2-3x-2
=6x^4+5x^3+(x^2+2x^2)-3x-2
=(6x^4+5x^3+x^2)+(2x^2-3x-2)
=x^2(2x+1)(3x+1)+(2x+1)(x-2)
=(2x+1)(3x^3+x^2+x-2)
=(2x+1)(3x^3-3+x^2+x+1)
=(2x+1)[3(x-1)(x^2+x+1)+x^2+x+1]
=(2x+1)(3x-2)(x^2+x+1)
3.x^4-11x^2+1
=(x^4-2x^2+1)-9x^2
=(x^2-1)^2-(3x)^2
=(x^2+3x-1)(x^2-3x-1)
4.2x^3-ax^2-5a^2x-2a^3
=2x^3-ax^2-(2a^2x+3a^2x)-2a^3
=(2x^3-2a^2x)-(ax^2+3a^2x+2a^3)
=2x(x+a)(x-a)-a(x+a)(x+2a)
=(x+a)[2x(x-a)-a(x+2a)]
=(x+a)[2x^2-3ax-2a^2]
=(x+a)(x-2a)(2x+a)
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