x的4次方 减6x的3次方 减37x的2次方 加66x 加216 因式分解

2025-04-07 16:35:52
推荐回答(1个)
回答1:

x^4-6x^3-37x^2+66x+216
=x^4-3x^3-3x^3+9x^2-46x^2+138x-72x+216

=x^3(x-3)-3x^2(x-3)-46x(x-3)-72(x-3)
=(x-3)(x^3-3x^2-46x-72)
=(x-3)(x^3-9x^2+6x^2-54x+8x-72)
=(x-3)(x^2(x-9)+6x(x-9)+8(x-9))
=(x-3)(x-9)(x^2+6x+8)
=(x-3)(x-9)(x+2)(x+4)