求:(X+1)(X+2)(X+3)(X+4)+1 因式分解

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求:(X+1)(X+2)(X+3)(X+4)+1因式分解求:(X+1)(X+2)(X+3)(X+4)+1因式分解求:(X+1)(X+2)(X+3)(X+4)+1因式分解=(x^2+5x+4)(x^2+

求:(X+1)(X+2)(X+3)(X+4)+1 因式分解
求:(X+1)(X+2)(X+3)(X+4)+1 因式分解

求:(X+1)(X+2)(X+3)(X+4)+1 因式分解
=(x^2+5x+4)(x^2+5x+6)+1
=(x^2+5x)^2+10(x^2+5x)+25
=(x^2+5x+5)^2

(x+1)(x+4)(x+2)(x+3)+1=[x^2+5x+4]*[x^2+5x+6]+1
((x^2+5x+4)(x^2+5x+4+2)+1
=(x^2+5x+4)^2+2(x^2+5x+4)+1
=(x^2+5x+4+1)^2 ==(x^2+5x+5)*(x^2+5x+5)
ok

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