因式分解x³-6x²-7x-6

因式分解x³-6x²-7x-6
因式分解x³-6x²-7x-6

因式分解x³-6x²-7x-6
原式=x^4-4x²-2x²-7x-6
=x²(x²-4)-(2x²+7x+6)
=x²(x+2)(x-2)-(x+2)(2x+3)
=(x+2)(x³-2x²-2x-3)
=(x+2)[(x³-3x²)+(x²-2x-3)]
=(x+2)[x²(x-3)+(x+1)(x-3)]
=(x+2)(x-3)(x²+x+1)