Divide: (5a^6+60a^5-20a^4)/(10a^4) (a^2)/(2)+60a^5-20a^4 (a^2)/(2)+6a-2 2a^2+6a-2 5a^6+6a-20a^4

## Step 1: Simplify the given expression<br />### The problem requires dividing \( \frac{5a^6 + 60a^5 - 20a^4}{10a^4} \). Start by splitting the numerator into separate terms divided by the denominator. This gives:<br />\[<br />\frac{5a^6}{10a^4} + \frac{60a^5}{10a^4} - \frac{20a^4}{10a^4}<br />\]<br />Simplify each term:<br />- \( \frac{5a^6}{10a^4} = \frac{5}{10}a^{6-4} = \frac{1}{2}a^2 \)<br />- \( \frac{60a^5}{10a^4} = \frac{60}{10}a^{5-4} = 6a \)<br />- \( \frac{20a^4}{10a^4} = \frac{20}{10}a^{4-4} = 2 \)<br /><br />Thus, the simplified result is:<br />\[<br />\frac{a^2}{2} + 6a - 2<br />\]<br /><br />## Step 2: Verify correctness of simplification<br />### Recheck each term to ensure no errors occurred during simplification:<br />- \( \frac{5a^6}{10a^4} = \frac{1}{2}a^2 \) (correct),<br />- \( \frac{60a^5}{10a^4} = 6a \) (correct),<br />- \( \frac{20a^4}{10a^4} = 2 \) (correct).<br /><br />The final simplified expression is confirmed as:<br />\[<br />\frac{a^2}{2} + 6a - 2<br />\]