求高手算算(x+6)(x+3)(x-1)(x-2)+3乘x的平方(因式分解)

2025-06-23 09:56:46
推荐回答(2个)
回答1:

(x+6)(x+3)(x-1)(x-2)+3x²
=(x+6)(x-1)(x+3)(x-2)+3x²
=(x²+5x-6)(x²+x-6)+3x²
=(x²+x-6)²+4x(x²+x-6)+3x²
=(x²+x-6+3x)(x²+x-6+x)
=(x²+4x-6)(x²+2x-6)
=[(x+2)²-10][(x+1)²-7]
=(x+2+√10)(x+2-√10)(x+1+√7)(x+1-√7)

回答2:

(x+6)(x+3)(x-1)(x-2)+3x²=x^4+6x³-6x²-36x+36+3x²=x^4+6x³-3x²-36x+36
=(x²+3x-6)²=[x+1.5-(√33)/2]²[x+1.5+(√33)/2]²