Answer :
To divide and simplify the expression [tex]\(\frac{2x^9 - 14x^6 + 4x^3}{-2x^5}\)[/tex], follow these steps:
1. Divide Each Term Individually: Start by dividing each term in the numerator by the term in the denominator, [tex]\(-2x^5\)[/tex].
- For [tex]\(2x^9\)[/tex]:
[tex]\[
\frac{2x^9}{-2x^5} = -x^{9-5} = -x^4
\][/tex]
- For [tex]\(-14x^6\)[/tex]:
[tex]\[
\frac{-14x^6}{-2x^5} = 7x^{6-5} = 7x
\][/tex]
- For [tex]\(4x^3\)[/tex]:
[tex]\[
\frac{4x^3}{-2x^5} = -2x^{3-5} = -\frac{2}{x^2}
\][/tex]
2. Combine Your Results: After dividing each term, combine the results to get the final simplified expression:
[tex]\[
-x^4 + 7x - \frac{2}{x^2}
\][/tex]
Therefore, the simplified form of [tex]\(\frac{2x^9 - 14x^6 + 4x^3}{-2x^5}\)[/tex] is [tex]\(-x^4 + 7x - \frac{2}{x^2}\)[/tex].
1. Divide Each Term Individually: Start by dividing each term in the numerator by the term in the denominator, [tex]\(-2x^5\)[/tex].
- For [tex]\(2x^9\)[/tex]:
[tex]\[
\frac{2x^9}{-2x^5} = -x^{9-5} = -x^4
\][/tex]
- For [tex]\(-14x^6\)[/tex]:
[tex]\[
\frac{-14x^6}{-2x^5} = 7x^{6-5} = 7x
\][/tex]
- For [tex]\(4x^3\)[/tex]:
[tex]\[
\frac{4x^3}{-2x^5} = -2x^{3-5} = -\frac{2}{x^2}
\][/tex]
2. Combine Your Results: After dividing each term, combine the results to get the final simplified expression:
[tex]\[
-x^4 + 7x - \frac{2}{x^2}
\][/tex]
Therefore, the simplified form of [tex]\(\frac{2x^9 - 14x^6 + 4x^3}{-2x^5}\)[/tex] is [tex]\(-x^4 + 7x - \frac{2}{x^2}\)[/tex].
