Question

Разложите на множители многочлен:
b²c²+c³-b³-bc
a³-3a²+a-3
8x³+2x²+4x+1
5a³c-a³+5bc-b

Answer 1

b²c²+c³-b³-bc=(b²c²+c³)-(b³+bc)=c²(b²+c)-b(b²+c)=(b²+c)(c²-b)
a³-3a²+a-3=(a³-3a²)+(a-3)=a²(a-3)+(a-3)=(a-3)(a²+1)
8x³+2x²+4x+1=(8x³+2x²)+(4x+1)=2x²(4x+1)+(4x+1)=(4x+1)(2x²+1)
5a³c-a³+5bc-b=(5a³c-a³)+(5bc-b)=a³(5c-1)+b(5c-1)=(5c-1)(a³+b)