Question

Представьте в виде произведения : х ^ 5 - х ^3 + х ^ 2 - 1 = m ^ 6 - m^4 + 2 m ^3 + 2 m ^2 =

Answer 1

$x^5-x^3+x^2-1=x^3(x^2-1)+1*(x^2-1)=(x^3+1)(x^2-1)=(x+1)(x^2-x+1)(x-1)(x+1)=(x+1)^2(x-1)(x^2-x+1)$

$m^6-m^4+2m^3+2m^2=m^4(m^2-1)+2m^2(m+1)=m^4(m-1)(m+1)+2m^2(m+1)=(m^5-1+2m^2)(m+1)=(m^5+m^4-m^4-m^3+m^3+m^2+m^2+m-m-1)(m+1)=(m^4(m+1)-m^3(m+1)+m^2(m+1)+m(m+1)-1*(m+1))(m+1)=(m^4-m^3+m^2+m-1)(m+1)(m+1)=(m^4-m^3+m^2+m-1)(m+1)^2$