解方程:6x^4-25x^3+12x^2+25x+6=0
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左==(6x^4 - 24x^3 + 24x^2) - x^3 - 12x^2 + 25x + 6
=6x^2*(x - 2)^2 - x^3 + 4x^2 - 4x - 16x^2 + 29x + 6
=6x^2*(x - 2)^2 - x(x^2 - 4x + 4) - (16x^2 - 29x - 6)
=6x^2*(x - 2)^2 - x(x - 2)^2 - (x - 2)(16x + 3)
=(x - 2)[6x^2*(x - 2) - x*(x - 2) - (16x + 3)]
=(x - 2)[6x^3 - 12x^2 - x^2 + 2x - 16x - 3]
=(x - 2)(6x^3 - 18x^2 + 5x^2 - 15x + x - 3)
=(x - 2)[6x^2*(x - 3) + 5x*(x - 3) + (x - 3)]
=(x - 2)(x - 3)(6x^2 + 5x + 1)
=(x - 2)(x - 3)(2x + 1)(3x + 1)
x1=2 x2=3 x3 =-1/2 x4=-1/3
=6x^2*(x - 2)^2 - x^3 + 4x^2 - 4x - 16x^2 + 29x + 6
=6x^2*(x - 2)^2 - x(x^2 - 4x + 4) - (16x^2 - 29x - 6)
=6x^2*(x - 2)^2 - x(x - 2)^2 - (x - 2)(16x + 3)
=(x - 2)[6x^2*(x - 2) - x*(x - 2) - (16x + 3)]
=(x - 2)[6x^3 - 12x^2 - x^2 + 2x - 16x - 3]
=(x - 2)(6x^3 - 18x^2 + 5x^2 - 15x + x - 3)
=(x - 2)[6x^2*(x - 3) + 5x*(x - 3) + (x - 3)]
=(x - 2)(x - 3)(6x^2 + 5x + 1)
=(x - 2)(x - 3)(2x + 1)(3x + 1)
x1=2 x2=3 x3 =-1/2 x4=-1/3
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