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`