餘式問題

[cally0119]

f(x)=x^30+x^14-x^5+4x^3+3x+1 除以(x^8-x^4)的餘式=?

[ellipse]

f(x)=x^30+x^14-x^5+4x^3+3x+1 除以(x^8-x^4)的餘式=?

x^8可改成x^4

x^30=(x^8)^3*x^6
=> (x^4)^3*x^6=x^12*x^6=x^8*x^8*x^2
=> x^4*x^4*x^2=x^8*x^2
=> x^4*x^2=x^6

x^14=(x^8)*x^6
=> x^4*x^6=x^8*x^2
=> x^4*x^2=x^6

所求=x^6+x^6-x^5+4x^3+3x+1
=2x^6-x^5+4x^3+3x+1