因式分解 1.x³－x－6 2.（x+y）²－x－y－1

题目

因式分解 1.x³－x－6 2.（x+y）²－x－y－1

答案

x³-x-6
=x²(x-2)+2x²-x-6
=x²(x-2)+2x(x-2)+3x-6
=x²(x-2)+2x(x-2)+3(x-2)
=(x-2)(x²+2x+3)
(x+y)²-x-y-1
=(x+y)²-(x+y)-1
=[(x+y)²-(x+y)+1/4]-5/4
=[(x+y)-1/2]²-5/4
=(x+y-1/2)²-(√5/2)²
=[(x+y-1/2)+√5/2][(x+y-1/2)-√5/2]
=(x+y-1/2+√5/2)(x+y-1/2-√5/2)