1. **State the problem:** Factor the polynomial $$6m^3 + 5mn + 6m^2 + 5n$$ by grouping. 2. **Group terms:** Group the polynomial into two pairs: $$ (6m^3 + 5mn) + (6m^2 + 5n) $$ 3. **Factor each group:** - From the first group $$6m^3 + 5mn$$, factor out the common factor $$m$$: $$ m(6m^2 + 5n) $$ - From the second group $$6m^2 + 5n$$, there is no common factor other than 1, so it remains as is. 4. **Rewrite the expression:** $$ m(6m^2 + 5n) + 1(6m^2 + 5n) $$ 5. **Factor out the common binomial:** $$ (6m^2 + 5n)(m + 1) $$ 6. **Final answer:** $$ 6m^3 + 5mn + 6m^2 + 5n = (6m^2 + 5n)(m + 1) $$ This shows the polynomial is factorable by grouping.