g) \( 4 a^{2}+15 a+9 \)

Did you know that the expression \( 4a^2 + 15a + 9 \) is a quadratic polynomial? Quadratics are fascinating because they can model a variety of real-world scenarios, such as projectile motion or profit maximization in business. The coefficients in the polynomial help determine the shape and direction of the parabola it represents! When factoring quadratics like this one, always look for two numbers that multiply to give the product of the leading coefficient (4) and the constant term (9), which is 36, while adding up to the middle term coefficient (15). A common mistake is overlooking rational roots or misidentifying the factors. Stay sharp and double-check your factors before concluding!