Question

Divide the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of a.

Divide 5a2 + 6a - 9 into 25a4 + 19a2 - a - 78.

Answer 1

We divide
`25a^4 + 19a^2 - a - 78` by
`5a^2 + 6a - 9` 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,
`5a^2 + 6a - 9` divided into
`25a^4 + 19a^2 - a - 78` gives
`5a^2 - 6a + 20` remainder -175a + 102.