1.求证:2的48次方减去1可以被63和65整除 2.分解因式;x的三次方减去3x加2

x³-3x+2
=x³-x-2x+2
=(x³-x)-2(x-1)
=x(x²-1)-2(x-1)
=x(x+1)(x-1)-2(x-1)
=(x-1)(x²+x-2)
=(x-1)(x-1)(x+2)
=(x-1)²(x+2)

1.证明:
2^48-1=(2^24+1)(2^24-1)
=(2^24+1)(2^12+1)(2^12-1)
=(2^24+1)(2^12+1)(2^6+1)(2^6-1)
=(2^24+1)(2^12+1)*65*63
则2的48次方减去1可以被63和65整除
2.分解因式;
x³-3x+2
=(x³-2x²+x)+2x²-4x+2
=x(x²-2x+1)+2(x²-2x+1)
=x(x-1)²+2(x-1)²
=(x-1)²(x+2)