Question: Directions: Read each problem carefully. Represent the situation with an algebraic expression, then factor the expression completely using the appropriate factoring technique. Show your complete solutions.
A. Factoring polynomial with Greatest Common Factor (GCF)
1. A rectangular park has an area represented by 15x^3 - 20x^2. Determine its dimensions by factoring.
1. **Problem:** A rectangular park has an area represented by $$15x^3 - 20x^2$$. We need to find its dimensions by factoring the expression.
2. **Formula and rules:** To factor a polynomial using the Greatest Common Factor (GCF), find the largest factor common to all terms and factor it out.
3. **Step-by-step solution:**
- Identify the GCF of the terms $$15x^3$$ and $$-20x^2$$.
- The coefficients 15 and 20 have a GCF of 5.
- The variable part: $$x^3$$ and $$x^2$$ have a GCF of $$x^2$$.
- So, the overall GCF is $$5x^2$$.
- Factor out $$5x^2$$:
$$15x^3 - 20x^2 = 5x^2(\cancel{3x} - \cancel{4})$$
- After factoring out, the expression inside the parentheses is $$3x - 4$$.
4. **Interpretation:** The dimensions of the rectangular park are $$5x^2$$ and $$3x - 4$$.
**Final answer:** The dimensions are $$5x^2$$ and $$3x - 4$$.