1. **State the problem:** Factor the polynomial $$g(x) = 3x^2 - 5x^4 + 2x - 7$$. 2. **Rewrite the polynomial in standard form:** Arrange terms in descending powers of $$x$$: $$g(x) = -5x^4 + 3x^2 + 2x - 7$$. 3. **Look for common factors:** There is no common factor for all terms. 4. **Try grouping:** Group terms to see if factoring by grouping is possible: $$(-5x^4 + 3x^2) + (2x - 7)$$. 5. **Factor each group if possible:** - From $$-5x^4 + 3x^2$$, factor out $$x^2$$: $$x^2(-5x^2 + 3)$$. - The second group $$2x - 7$$ cannot be factored further. 6. **Check if the expression can be factored further:** Since the two groups do not share a common binomial factor, factoring by grouping is not possible. 7. **Conclusion:** The polynomial $$g(x) = 3x^2 - 5x^4 + 2x - 7$$ cannot be factored further over the integers. **Final answer:** $$g(x) = -5x^4 + 3x^2 + 2x - 7$$ (already simplified, no factorization possible).