1. **State the problem:** Simplify the expression $6m^4 + 7m^2 - 20$ or factor it if possible. 2. **Look for common factors:** There is no common factor for all terms. 3. **Try to factor the polynomial:** Let $x = m^2$, then the expression becomes $6x^2 + 7x - 20$. 4. **Use the quadratic factoring method:** We want two numbers that multiply to $6 \times (-20) = -120$ and add to $7$. 5. The numbers are $15$ and $-8$ because $15 \times (-8) = -120$ and $15 + (-8) = 7$. 6. Rewrite the middle term: $$6x^2 + 15x - 8x - 20$$ 7. Factor by grouping: $$3x(2x + 5) - 4(2x + 5)$$ 8. Factor out the common binomial: $$(3x - 4)(2x + 5)$$ 9. Substitute back $x = m^2$: $$(3m^2 - 4)(2m^2 + 5)$$ **Final answer:** $$6m^4 + 7m^2 - 20 = (3m^2 - 4)(2m^2 + 5)$$