Replace [tex]a^2=b[/tex]. Then
[tex]8a^6+10a^4+2\equiv8b^3+10b^2+2[/tex]
By the remainder theorem, the remainder upon dividing this polynomial by [tex]a^2+3\equiv b+3[/tex] is given by the value of the polynomial where [tex]b=-3[/tex]. We have
[tex]8(-3)^3+10(-3)^2+2=8(-27)+10(9)+2=-124[/tex]
