分解因式：8x^4+6x^3-19x^2+3x+2，要详细过程
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8x^4+6x^3-19x^2+3x+2
=(8x^4-8x^2)+(6x^3-6x^2)-(3x^2-3x)-(2x^2-2)
=8x^2(x^2-1)+6x^2(x-1)-3x(x-1)-2(x^2-1)
=8x^2(x-1)(x+1)+6x^2(x-1)-3x(x-1)-2(x-1)(x+1)
=(x-1)[8x^2(x+1)+6x^2-3x-2(x+1)]
=(x-1)(8x^3+8x^2+6x^2-3x-2x-2)
=(x-1)(8x^3+14x^2-5x-2)
=(x-1)[(8x^3+16x^2)-(2x^2+4x)-(x+2)]
=(x-1)[8x^2(x+2)-2x(x+2)-(x+2)]
=(x-1)(x+2)(8x^2-2x-1)
=(x-1)(x+2)(4x+1)(2x-1)
=(8x^4-8x^2)+(6x^3-6x^2)-(3x^2-3x)-(2x^2-2)
=8x^2(x^2-1)+6x^2(x-1)-3x(x-1)-2(x^2-1)
=8x^2(x-1)(x+1)+6x^2(x-1)-3x(x-1)-2(x-1)(x+1)
=(x-1)[8x^2(x+1)+6x^2-3x-2(x+1)]
=(x-1)(8x^3+8x^2+6x^2-3x-2x-2)
=(x-1)(8x^3+14x^2-5x-2)
=(x-1)[(8x^3+16x^2)-(2x^2+4x)-(x+2)]
=(x-1)[8x^2(x+2)-2x(x+2)-(x+2)]
=(x-1)(x+2)(8x^2-2x-1)
=(x-1)(x+2)(4x+1)(2x-1)
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