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Your task involves formulating two real-life problems related to factoring polynomials and solving them completely. Let me help you with both parts.

### Problem 1: Area of a Rectangular Garden
A gardener wants to build a rectangular garden and knows that the total area of the garden will be given by the polynomial expression \( x^2 + 5x + 6 \), where \( x \) represents some measurement of the garden's length in meters. The width of the garden is another factor of the polynomial. 

**Question:** What are the possible dimensions of the garden?

#### Solution:
We factor the quadratic expression \( x^2 + 5x + 6 \):

\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]

Thus, the dimensions of the garden are \( x + 2 \) meters and \( x + 3 \) meters.

### Problem 2: Revenue Calculation for a Business
A company’s revenue in dollars is modeled by the polynomial expression \( x^2 + 7x + 10 \), where \( x \) represents the number of units sold. 

**Question:** What are the possible factors that contribute to the company’s revenue?

#### Solution:
We factor the polynomial \( x^2 + 7x + 10 \):

\[
x^2 + 7x + 10 = (x + 2)(x + 5)
\]

Thus, the factors contributing to the revenue are \( x + 2 \) and \( x + 5 \), which may represent the pricing model or number of units sold.

Would you like further details or have any specific questions?

### Related Questions:
1. What is the importance of factoring polynomials in real-life applications?
2. How can we apply polynomial factoring in optimizing construction projects?
3. Can you formulate a similar problem related to physics or economics involving polynomials?
4. What are the key techniques to factor a quadratic polynomial quickly?
5. How does the distributive property relate to factoring polynomials?

### Tip:
Always check if the quadratic expression can be factored by looking for factors of the constant term that add up to the middle coefficient.

Formulate two (2) real-life problems involving factors of polynomials and solve the problems you formulate accurately and show the complete solution.

Learn how to formulate and solve real-life problems by factoring quadratic polynomials, such as calculating garden area and business revenue. This tutorial is designed for Grade 8 students, covering key algebraic techniques for factoring quadratic equations.

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