To divide the expression [tex]\(\frac{14 m^2 - 28 m^8 - 7 m}{7 m}\)[/tex], follow these steps:
1. Factor the numerator and denominator:
The numerator is [tex]\(14 m^2 - 28 m^8 - 7 m\)[/tex] and the denominator is [tex]\(7 m\)[/tex].
2. Separate the terms in the numerator and divide each by the denominator:
[tex]\[
\frac{14 m^2}{7 m} - \frac{28 m^8}{7 m} - \frac{7 m}{7 m}
\][/tex]
3. Simplify each term individually:
- For the first term: [tex]\(\frac{14 m^2}{7 m}\)[/tex]
[tex]\[
14 m^2 \div 7 m = 2 m
\][/tex]
- For the second term: [tex]\(\frac{28 m^8}{7 m}\)[/tex]
[tex]\[
28 m^8 \div 7 m = 4 m^7
\][/tex]
- For the third term: [tex]\(\frac{7 m}{7 m}\)[/tex]
[tex]\[
7 m \div 7 m = 1
\][/tex]
4. Rewrite the simplified terms together:
[tex]\[
2 m - 4 m^7 - 1
\][/tex]
Therefore, the simplified expression is:
[tex]\[
2 m - 4 m^7 - 1
\][/tex]
The correct answer is:
C) [tex]\(2 m - 4 m^7\)[/tex]
