Ответ:

f(x)=(x-1)³(x+2)²

Объяснение:

f(x)=x⁵+x⁴-5x³-x²+8x-4=x⁵-x⁴+2x⁴-2x³-3x³+3x²-4x²+4x+4x-4=

=x⁴(x-1)+2x³(x-1)-3x²(x-1)-4x(x-1)+4(x-1)=(x-1)(x⁴+2x³-3x²-4x+4)=

=(x-1)[(x⁴-4x²+4)+2x(x²-2)+x²]=(x-1)[(x²-2)²+2x(x²-2)+x²]=(x-1)[x²-2+x]²=

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

=(x-1)³(x+2)²