Question

分解因式：(x²+x+1)(x²+x+2)-12 尽快啊，5分钟内

Answer 1

(x²+x+1)(x²+x+2)-12 (把x^2+x看成一个整体)

=(x^2+x)^2+3(x^2+x)-10
=(x^2+x+5)(x^2+x-2)
=(x^2+x+5)(x+2)(x-1)

Answer 2

(x²+x+1)(x²+x+2)-12

=【x²+x】²＋3【x²+x】-10
=【x²+x-2】【x²+x＋5】
=【x-1】【x＋2】【x²+x＋5】

Answer 3

：(x²+x+1)(x²+x+2)-12
=(x²+x)²+3(x²+x)+2-12
=(x²+x)²+3(x²+x)-10
=(x²+x+5)(x²+x-2)
=(x²+x+5)(x+2)(x-1)

Answer 4

令a=x²+x
则原式=(a+1)(a+2)-12
=a²+3a+2-12
=a²+3a-10
=(a+5)(a-2)
=(x²+x+5)(x²+x-2)
=(x²+x+5)(x+2)(x-1)

Answer 5

(x²+x+1)(x²+x+2)-12
=(x²+x+1)[(x²+x+1)+1]-12
=(x²+x+1)²+(x²+x+1)-12
=(x²+x+1+4)(x²+x+1-3)
=(x²+x+5)(x²+x-2)
=(x²+x+5)(x+2)(x-1)