求难一点的因式分解题。附答案的

Question

如题所述

Answer 1

这是我刚刚回答的4个因式分解，试试看①x³+4x²-9;
=x³+3x²+x²-9
=x²(x+3)+(x+3)(x-3)
=(x+3)(x²+x-3)

②x³+5x²-18;
=x³+3x²+2x²-18
=x²(x+3)+2(x+3)(x-3)
=(x+3)(x²+2x-6)

③x³+6x²+11x+6;
=x³+6x²+9x+2x+6
=x(x+3)²+2(x+3)
=(x+3)(x²+3x+2)
=(x+3)(x+2)(x+1)

④x³-11x²+31x-21.
=x³-x²-10x²+10x+21x-21
=x²(x-1)-10x(x-1)+21(x-1)
=(x-1)(x²-10x+21)
=(x-1)(x-3)(x-7)其实会者不难，难者不会，

Answer 2

x³+y³+z³-3xyz
=x³+3x²y+3xy²+y³+z³-3x²y-3xy²-3xyz
=(x+y)³+z³-3xy(x+y+z)
=(x+y+z)(x²+2xy+y²-xz-yz+z²)-3xy(x+y+z)
=(x+y+z)(x²+y²+z²-xy-xz-yz)