https://file.aiquickdraw.com/mathbot/file/1725496735142bkegtvqx.jpg

Your task is to:

1. Formulate two real-life problems involving the factors of polynomials.
2. Solve these problems accurately and show the complete solution.

### Here are two example problems and their solutions:

#### Problem 1:
**Situation:** You are planning to create a rectangular garden, and you know that the area of the garden is represented by the polynomial \( A(x) = x^2 + 5x + 6 \), where \(x\) is the width in meters.

**Task:** Factor the polynomial to determine the possible dimensions of the garden.

**Solution:**
1. Factor the polynomial \( x^2 + 5x + 6 \).
   \[
   A(x) = (x + 2)(x + 3)
   \]
2. The factors give the possible dimensions of the garden. So, the width is \( x + 2 \) meters and the length is \( x + 3 \) meters.

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

---

#### Problem 2:
**Situation:** A box has a volume that can be represented by the polynomial \( V(x) = x^3 - 7x^2 + 10x \), where \(x\) represents the height of the box.

**Task:** Factor the polynomial to determine the possible dimensions of the box.

**Solution:**
1. Factor the polynomial \( x^3 - 7x^2 + 10x \).
   \[
   V(x) = x(x^2 - 7x + 10)
   \]
2. Now, factor \( x^2 - 7x + 10 \) further:
   \[
   V(x) = x(x - 5)(x - 2)
   \]
3. The factors \(x\), \(x-5\), and \(x-2\) represent the possible dimensions of the box. So, the height could be \( x \), the width \( x-5 \), and the length \( x-2 \).

Thus, the possible dimensions of the box are \( x \), \( x-5 \), and \( x-2 \).

---

Would you like more details or have any questions? 

Here are 5 questions to expand on these concepts:
1. How do you determine if a polynomial can be factored easily?
2. Can every polynomial be factored, or are there exceptions?
3. What real-life scenarios might involve higher-degree polynomials?
4. How can factoring help in solving quadratic equations?
5. What are some common methods for factoring polynomials?

**Tip:** When factoring polynomials, always check if there’s a common factor across all terms first!

Formulate two (2) real-life problems involving factors of polynomials and solve the problems accurately with complete solutions.

Learn how to formulate and solve real-life problems involving factors of polynomials. This guide covers key algebraic concepts, including polynomial factoring techniques and the zero-product property, tailored for Grade 8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation