1. **State the problem:** Factor the quadratic polynomial $$2x^2 + 9x + 7$$ into the form $$(ax + b)(cx + d)$$. 2. **Recall the factoring method:** For a quadratic $ax^2 + bx + c$, find two numbers that multiply to $a \times c$ and add to $b$. 3. **Calculate product and sum:** Here, $a=2$, $b=9$, $c=7$. So, product = $$2 \times 7 = 14$$ and sum = $$9$$. 4. **Find two numbers:** The numbers that multiply to 14 and add to 9 are $$7$$ and $$2$$. 5. **Rewrite the middle term:** $$2x^2 + 7x + 2x + 7$$. 6. **Group terms:** $$(2x^2 + 7x) + (2x + 7)$$. 7. **Factor each group:** $$x(2x + 7) + 1(2x + 7)$$. 8. **Factor out common binomial:** $$(x + 1)(2x + 7)$$. 9. **Final answer:** The factors are $$(x+1)(2x+7)$$. This means the polynomial factors as $$(x+1)(2x+7)$$.