Question

设ax^3+bx^2+cx+d能被x^2+h^2(h不等于0)整除,则

Answer 1

ax^3+bx^2+cx+d能被x^2+h^2整除

则有

ax^3+bx^2+cx+d

=(x^2+h^2)*(mx+n)

=mx^3+nx^2+h^2mx+h^2*n

所以有a=m,b=n,c=h^2m,d=h^2n

即c=h^2*a

d=h^2*b

即ad=bc