1. **State the problem:** Factor the polynomial $$4x^2 + 12x + 9$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two binomials $$(mx + n)(px + q)$$ such that $$mp = a$$, $$nq = c$$, and $$mq + np = b$$. 3. **Identify coefficients:** Here, $$a=4$$, $$b=12$$, and $$c=9$$. 4. **Find factors of $$a$$ and $$c$$:** - Factors of $$4$$: $$1, 4, 2$$ - Factors of $$9$$: $$1, 9, 3$$ 5. **Try possible combinations:** - Try $$(2x + 3)(2x + 3)$$: - Multiply: $$2x \times 2x = 4x^2$$ - Outer and inner: $$2x \times 3 + 3 \times 2x = 6x + 6x = 12x$$ - Last: $$3 \times 3 = 9$$ 6. **Check sum:** The middle term is $$12x$$, which matches the original polynomial. 7. **Write the factorization:** $$4x^2 + 12x + 9 = (2x+3)(2x+3)$$ or $$ (2x+3)^2 $$. **Final answer:** Factors: (2x+3)(2x+3)