The factored form of the expression is:

$1.5 \left( \frac{1}{3} x^{-\frac{1}{2}} \sqrt{3x + 4} + x^{\frac{1}{2}} (3x + 4)^{-\frac{1}{2}} \right)$

This is the simplest form after factoring. Let me know if you'd like further explanation or details on any part of this!

Here are some related questions to explore further:

1. How can we simplify fractional exponents?
2. What are the steps to factor more complex algebraic expressions?
3. How does factoring help in solving equations?
4. Can we apply this to solve equations involving square roots?
5. What other factoring methods are useful in calculus?

Tip: When dealing with fractional powers, always consider common factors for simplification!