（x+1)(x+2)(x+3)(x+4)+x(x+5)因式分解

您好：

(X+1)(X+2)(X+3)(X+4)+X(X+5)=[(X+1)(X+4)][(X+2)(X+3)]+X(X+5)
=(X^2+5X+6)(X^2+5X+4)+(X^2+5X)
=(X^2+5X)^2+10(X^2+5X)+24+(X^2+5X)
=(X^2+5X)^2+11(X^2+5X)+24
=(X^2+5X+3)(X^2+5X+8)

不明白，可以追问
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祝学习进步！

(X+1)(X+2)(X+3)(X+4)+X(X+5)=[(X+1)(X+4)][(X+2)(X+3)]+X(X+5)
=(X²+5X+6)(X²+5X+4)+(X²+5X)
=(X²+5X)²+10(X²+5X)+24+(X²+5X)
=(X²+5X)²+11(X²+5X)+24
=(X²+5X+3)(X²+5X+8)
=(x+2.5+√13/2)(x+2.5-√13/2)(X²+5X+8)

（x+1)(x+2)(x+3)(x+4)+x(x+5)解原式 =[(X+1)(X+4)][(X+2)(X+3)]+X(X+5)
=(X^2+5X+6)(X^2+5X+4)+(X^2+5X)
=(X^2+5X)^2+10(X^2+5X)+24+(X^2+5X)
=(X^2+5X)^2+11(X^2+5X)+24
=(X^2+5X+3)(X^2+5X+8)