(x+1)(x+2)(x+3)(x-4)+36分解因式……

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(x+1)(x+2)(x+3)(x-4)+36分解因式……(x+1)(x+2)(x+3)(x-4)+36分解因式……(x+1)(x+2)(x+3)(x-4)+36分解因式……(x+1)(x+2)(x+

(x+1)(x+2)(x+3)(x-4)+36分解因式……
(x+1)(x+2)(x+3)(x-4)+36
分解因式……

(x+1)(x+2)(x+3)(x-4)+36分解因式……
(x+1)(x+2)(x+3)(x+4)+36
=[(x+1)(x+4)][(x+2)(x+3)]+36
=(x²+5x+4)(x²+5x+6)+36
=(x²+5x)²+10(x²+5x)+60
=(x²+5x)²+10(x²+5x)+25+35
=(x²+5x+5)²+35 /实数范围内无法分解,如果是复数范围,继续:
=(x²+5x+5+√35i)(x²+5x+5-√35i)

实数范围内无法分解因式,理由见下:
令f(x)=(x+1)(x+2)(x+3)(x-4)+36=...+12
12的因数有±1,±2,±3,±4,±6,±12,±24
其中用这些因数去试探f(x)的值,都不等于0,所以实数范围内无法分解f(x)

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