Answer:
-18x - 7 + 6x^7 - 6x^9 + 18x^9
Explanation:
To complete the division problem and find the remainder, we need to divide the dividend by the divisor. In this case, the dividend is -18x - 7 and the divisor is 2x^3 - 2x^5 + 6x^5.
When performing the division, we start by dividing the highest degree term of the dividend by the highest degree term of the divisor. So we divide -18x by 6x^5, which gives us -3x^4. We then multiply this term by the entire divisor: -3x^4 * (2x^3 - 2x^5 + 6x^5), which gives us -6x^7 + 6x^9 - 18x^9.
Next, we subtract this result from the original dividend:
-18x - 7 - (-6x^7 + 6x^9 - 18x^9)
Simplifying the expression, we get:
-18x - 7 + 6x^7 - 6x^9 + 18x^9
At this point, we cannot divide any further because the highest degree term of the divisor is x^5 and the highest degree term in the updated expression is x^9. Therefore, the division process ends here, and the remainder is the expression: -18x - 7 + 6x^7 - 6x^9 + 18x^9.