Question

find the remainder when 8a^6+10a^4+2 is divided by a^2+3 by using remainder theorem

Answer 1

Replace $a^2=b$. Then

$8a^6+10a^4+2\equiv8b^3+10b^2+2$

By the remainder theorem, the remainder upon dividing this polynomial by $a^2+3\equiv b+3$ is given by the value of the polynomial where $b=-3$. We have

$8(-3)^3+10(-3)^2+2=8(-27)+10(9)+2=-124$