Question

因式分解：帮个忙 x^3+3x^2+3x-26 x^4-4x+3 a^4+2a^3+2a^2+2a+1 x^3-7x+6 x^3+4x-13x-24 x^4-11x+1

Answer 1

x^3+3x^2+3x-26
=(x+1)^3-3^3
=(x+1-3)((x+1)^2+3(x+1)+3^2)
=(x-2)(x^2+5x+13)

x^4-4x+3
x^4-4x+3
=(x^4-x)-(3x-3)
=x(x^3-1)-3(x-1)
=x(x-1)(x^2+x+1)-3(x-1)
=(x-1)(x^3+x^2+x-3)
=(x-1)[(x^3-1)+(x^2-1)+(x-1)]
=(x-1)[(x-1)(x^2+x+1)+(x-1)(x+1)+(x-1)]
=(x-1)^2[(x^2+x+1)+(x+1)+1]
=(x-1)^2(x^2+2x+3)

a^4+2a^3+2a^2+2a+1
=(a^4+2a^3+a^2)+(a^2+2a+1)
=a^2(a+1)^2+(a+1)^2
=(a+1)^2(a^2+1)

x^3 -7x +6
=x^3-x-6(x-1)
=x(x+1)(x-1)-6(x-1)
=(x-1)(x*x+x-6)
=(x-1)(x+3)(x-2)

x^3+4x^2-13x-24
=(x^3-27)+(4x^2-13x+3)
=(x-3)(x^2+3x+9)+(4x-1)(x-3)
=(x-3)(x^2+3x+9+4x-1)
=(x-3)(x^2+7x+8)

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)

Answer 2

x^3+3x^2+3x-26 =（x-2)(x²+5x+13), x^4-4x+3 =(x-1)(x³+x²+x-3)=(x-1)(x-1)(x²+2x+3）,a^4+2a^3+2a^2+2a+1=(a+1)(a³+a²+a+1)=(a+1)(a+1)(a²+1）
x^3-7x+6 =（x-1)(x²+x-6)=(x-1)(x-2)(x+3)
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Answer 3

什么程度的题？要是中学的，就找有理根吧