1. **State the problem:** Factor the expression $20m^3 + 2m - 6m^2$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in all terms. 3. **Find the GCF:** The terms are $20m^3$, $2m$, and $-6m^2$. The coefficients are 20, 2, and 6. The GCF of 20, 2, and 6 is 2. Each term contains at least one $m$, so the variable part of the GCF is $m$. Thus, the GCF is $2m$. 4. **Factor out the GCF:** $$20m^3 + 2m - 6m^2 = 2m(\cancel{10m^2} + \cancel{1} - \cancel{3m})$$ Here, we cancel the common factor $2m$ from each term inside the parentheses. 5. **Rewrite the expression:** $$= 2m(10m^2 + 1 - 3m)$$ 6. **Rearrange terms inside parentheses for clarity:** $$= 2m(10m^2 - 3m + 1)$$ 7. **Check if the quadratic $10m^2 - 3m + 1$ can be factored further:** Calculate the discriminant: $$\Delta = (-3)^2 - 4 \times 10 \times 1 = 9 - 40 = -31$$ Since $\Delta < 0$, the quadratic does not factor over the real numbers. 8. **Final factored form:** $$\boxed{2m(10m^2 - 3m + 1)}$$