To solve [tex]\((14 m^4 - 21 m^3 - 28 m^2) \div 7 m^2\)[/tex], let's divide each term of the polynomial by [tex]\(7 m^2\)[/tex] step-by-step:
1. Divide the first term [tex]\(14 m^4\)[/tex] by [tex]\(7 m^2\)[/tex]:
[tex]\[
\frac{14 m^4}{7 m^2} = \frac{14}{7} \cdot \frac{m^4}{m^2} = 2 \cdot m^{4-2} = 2 m^2
\][/tex]
2. Divide the second term [tex]\(-21 m^3\)[/tex] by [tex]\(7 m^2\)[/tex]:
[tex]\[
\frac{-21 m^3}{7 m^2} = \frac{-21}{7} \cdot \frac{m^3}{m^2} = -3 \cdot m^{3-2} = -3 m
\][/tex]
3. Divide the third term [tex]\(-28 m^2\)[/tex] by [tex]\(7 m^2\)[/tex]:
[tex]\[
\frac{-28 m^2}{7 m^2} = \frac{-28}{7} \cdot \frac{m^2}{m^2} = -4 \cdot m^{2-2} = -4 \cdot m^0 = -4 \cdot 1 = -4
\][/tex]
Combining these results, we get:
[tex]\[
\frac{14 m^4 - 21 m^3 - 28 m^2}{7 m^2} = 2 m^2 - 3 m - 4
\][/tex]
Thus, the simplified form of [tex]\(\left(14 m^4 - 21 m^3 - 28 m^2\right) \div 7 m^2\)[/tex] is:
[tex]\[
2 m^2 - 3 m - 4
\][/tex]
