把(x^2+3x+2)(x^2-9x+20)-72因式分解

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把(x^2+3x+2)(x^2-9x+20)-72因式分解
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把(x^2+3x+2)(x^2-9x+20)-72因式分解
把(x^2+3x+2)(x^2-9x+20)-72因式分解

把(x^2+3x+2)(x^2-9x+20)-72因式分解
原式=(x+1)(x+2)(x-4)(x-5)-72
=[(x+1)(x-4)]*[(x+2)(x-5)]-72
=[x^2-3x-4]*[x^2-3x-10]-72
=(x^2-3x)^2-14(x^2-3x)+40-72
=(x^2-3x)^2-14(x^2-3x)-32
=(x^2-3x-16)(x^2-3x+2)
=(x^2-3x-16)(x-1)(x-2)

原式=(x+2)(x+1)(x-4)(x-5)-72


(x^2+3x+2)(x^2-9x+20)-72
=(x+2)(x+1)(x-4)(x-5)-72
=(x+2)(x-5)(x+1)(x-4)-72
=(x^2-3x-10)(x^2-3x-4)-72
=(x^2-3x)^2-14(x^2-3x)-32
=(x^2-3x-16)(x^2-3x+2)
=(x^2-3x-16)(x-2)(x-1...

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(x^2+3x+2)(x^2-9x+20)-72
=(x+2)(x+1)(x-4)(x-5)-72
=(x+2)(x-5)(x+1)(x-4)-72
=(x^2-3x-10)(x^2-3x-4)-72
=(x^2-3x)^2-14(x^2-3x)-32
=(x^2-3x-16)(x^2-3x+2)
=(x^2-3x-16)(x-2)(x-1)
解法2:
另x^2-3x=y,则
(x^2+3x+2)(x^2-9x+20)-72
=(y+6x+2)(y-6x+20)-72
=y^2+22y+(-36x^2+108x)-32
=y^2+22y-36y-32=y^2-14y-32
=(y-16)(y+2)
=(x^2-3x-16)(x^2-3x+2)
=(x-1)(x-2)(x^2-3x-16).

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