因式分解,：①x^5+x+1=?②x³-9x+8=?③a⁴+2a³+3a²+2a+1=?④x(x-1)+y(y+1)-2xy=?⑤(x²+3x)²-2(x²+3x)-8=?

因式分解,：①x^5+x+1=?②x³-9x+8=?③a⁴+2a³+3a²+2a+1=?④x(x-1)+y(y+1)-2xy=?⑤(x²+3x)²-2(x²+3x)-8=?
因式分解,
：①x^5+x+1=?②x³-9x+8=?③a⁴+2a³+3a²+2a+1=?④x(x-1)+y(y+1)-2xy=?⑤(x²+3x)²-2(x²+3x)-8=?

因式分解,：①x^5+x+1=?②x³-9x+8=?③a⁴+2a³+3a²+2a+1=?④x(x-1)+y(y+1)-2xy=?⑤(x²+3x)²-2(x²+3x)-8=?
①x^5+x+1
=x^5-x²+x²+x+1
=x²(x³-1)+(x²+x+1)
=x²(x-1)(x²+x+1)+(x²+x+1)
=(x²+x+1)[x²(x-1)+1]
=(x²+x+1)(x³-x²+1)
②x³-9x+8
=x³-x-8x+8
=x(x²-1)-8(x-1)
=x(x+1)(x-1)-8(x-1)
=(x-1)(x²+x-8)
③a⁴+2a³+3a²+2a+1 整理
=(a⁴+2a³+a²)+(2a²+2a)+1
=a²(a²+2a+1)+2a(a+1)+1
=a²(a+1)²+2a(a+1)+1 完全平方
=[a(a+1)+1]²
=(a²+a+1)²
④x(x-1)+y(y+1)-2xy
=x²-x+y²+y-2xy 整理
=(x²-2xy+y²)-(x-y)
=(x-y)²-(x-y)
=(x-y)(x-y-1)
⑤(x²+3x)²-2(x²+3x)-8
十字相乘
=[(x²+3x)-4][(x²+3x)+2]
=(x²+3x-4)(x²+3x+2) 十字相乘
=(x-1)(x+4)(x+1)(x+2)