因式分解 6x^4-25x^3+12x^2+25x+6
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6x^4-25x^3+12x^2+25x+6
=6(x^2-1)^2-25x(x^2-1)+24x^2
=[3(x^2-1)-8x][2(x^2-1)-3x]
=(3x^2-8x-3)(2x^2-3x-2)
=(3x+1)(x-3)(2x+1)(x-2)
=6(x^2-1)^2-25x(x^2-1)+24x^2
=[3(x^2-1)-8x][2(x^2-1)-3x]
=(3x^2-8x-3)(2x^2-3x-2)
=(3x+1)(x-3)(2x+1)(x-2)
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=(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)
=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)
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