Question

数学分解因式

1. x²＋x³－2
2. x³＋y³＋z³－3xyz
3. x^6＋8x³＋9
4. 3x³－6x²＋3 请写过程

Answer 1

x²＋x³－2
=(x²-1)+(x³－1)
=(x +1)(x-1)+(x-1)(x²＋x+1)
=(x-1)[(x +1)+(x²＋x+1)]
=(x-1)(x²＋2x+2)

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

x^6＋9x³+8
=(x³+1)(x³+8)
=(x+1)(x+2)(x²-x+1)(x²-2x+4)

4. 3x³－6x²＋3
=3x³-6x²+3x-3x+3
=3x(x-1)²-3(x-1)
=3(x-1)(x²-x-1)

Answer 2

1: =(x²-1)+(x³－1)
=(x +1)(x-1)+(x-1)(x²＋x+1)
=(x-1)[(x +1)+(x²＋x+1)]
=(x-1)(x²＋2x+2)

Answer 3

1254466=5446620