To solve this problem, we use synthetic division.
8x^4 + 6x^2 - 7 | 2x^2
-8x^4 4x^2 + 3
0 6x^2 - 7
-6x^2
0 -7
Now, we use the division algorithm to find the equivalence.
Therefore, the division is equal to
[tex]\frac{8x^4+6x^2-7}{2x^2}=4x^2+3-\frac{7}{2x^2}[/tex]Where 4x^2 + 3 is the quotient, -7 is the remaining part and 2x^2 is the divisor.