數學上的問題-0- remainder theorem

Let f(x) = x^99 +k
When f(x) is divided by x+1, the remainder is 1.
Hence, find the remainder when 9^99 is divided by 10.Solx+1=0x=－1f(－1)=(－1)^99+k=k－1=1k=2f(x)=x^99+2x^99+2=q(x)(x+1)+19^99+2=q(9)*10+19^99=[q(9)－1]*10+9the remainder when 9^99 is divided by 10.is 9