We divide [tex]25a^4 + 19a^2 - a - 78[/tex] by [tex]5a^2 + 6a - 9[/tex] using the long division algorithm as follows:
5a^2 - 6a + 20
_____________________
5a^2 + 6a - 9 | 25a^4 + 0a^3 + 19a^2 - a - 78
| 25a^4 + 30a^3 - 45a^2
|___________________
| -30a^3 + 64a^2 - a - 78
| -30a^3 - 36a^2 + 54a
| ____________________
| 100a^2 - 55a - 78
| 100a^2 + 120a - 180
| __________________
-175a + 102
Therefore, [tex]5a^2 + 6a - 9[/tex] divided into [tex]25a^4 + 19a^2 - a - 78[/tex] gives [tex]5a^2 - 6a + 20[/tex] remainder -175a + 102.
