分解因式(x²+2x-3)(x²+2x-24)+90

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分解因式(x²+2x-3)(x²+2x-24)+90

(x²+2x-3)(x²+2x-24)+90
=(x²+2x)²-27(x²+2x)+72+90
=(x²+2x)²-27(x²+2x)+162
=(x²+2x-9)(x²+2x-18)
如有不明白,可以追问
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令a=x²+2x
原式=(a-3)(a-24)+90
=a²-27a+72+90
=a²-27a+162
=(a-9)(a-18)
=(x²+2x-9)(x²+2x-18)

(x²+2x-3)(x²+2x-24)+90=(x²+2x-3)(x²+2x-3-21)+90=(x²+2x-3)²-21(x²+2x-3)+90
=(x²+2x-3-15)(x²+2x-3-6)=(x²+2x-18)(x²+2x-9)