因式分解4x^3-8x^2+3x-6 x^4-15x^2-10x+24？
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原式=4x²(x-2)+3(x-2)
=(x-2)(4x²+3)
原式=x^4-1-(15x²+10x-25)
=(x²+1)(x²-1)-5(3x²+2x-5)
=(x²+1)(x+1)(x-1)-5(3x+5)(x-1)
=(x-1)(x³+x²+x+1-15x-25)
=(x-1)(x³+x²-14x-24)
=(x-1)(x³-16x+x²+2x-24)
=(x-1)[x(x+4)(x-4)+(x-4)(x+6)]
=(x-1)(x-4)(x²+5x+6)
=(x-1)(x-4)(x+2)(x+3)
=(x-2)(4x²+3)
原式=x^4-1-(15x²+10x-25)
=(x²+1)(x²-1)-5(3x²+2x-5)
=(x²+1)(x+1)(x-1)-5(3x+5)(x-1)
=(x-1)(x³+x²+x+1-15x-25)
=(x-1)(x³+x²-14x-24)
=(x-1)(x³-16x+x²+2x-24)
=(x-1)[x(x+4)(x-4)+(x-4)(x+6)]
=(x-1)(x-4)(x²+5x+6)
=(x-1)(x-4)(x+2)(x+3)
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