Question

因式分解x^4+3x^3-3x^2-12x-4

Answer 1

x^4+3x^3-3x^2-12x-4
=x^4-4x^2+3x^3-12x+x^2-4
=x^2(x^2-4)+3x(x^2-4)+(x^2-4)
=(x^2-4)(x^2+3x+1)
=(x+2)(x-2)(x^2+3x+1)有理数范围到此结束
=(x+2)(x-2)(x^2+3x+(3/2)^2-9/4+1)
=(x+2)(x-2)[(x+3/2)^2-5/4)]
=(x+2)(x-2)(x+3/2+√5/2)(x+3/2-√5/2)

Answer 2

x^4+3x^3-3x^2-12x-4
=（x^4+3x^3-10x^2)+7x^2-12x-4
=x^2(x^2+3x-10)+(7x+2)(x-2)
=x^2(x+5)(x-2)+(7x+2)(x-2)
=(x-2)(x^3+5x^2+7x+2)
=(x-2)(x^3+2x^2+3x^2+7x+2)
=(x-2)[x^2(x+2)+（3x+1)(x+2)]
=(x-2)(x+2)(x^2+3x+1)

Answer 3

x^4+3x^3-3x^2-12x-4
=x^4+3x^3+2x^2-5x^2-12x-4
=x²(x²+3x+2)-(5x^2+12x+4)
=x²(x+2)(x+1)-(5x+2)(x+2)
=(x+2)[x²(x+1)-(5x+2)]
=(x+2)(x³+x²-5x+2)