https://file.aiquickdraw.com/mathbot/file/1727176914061enl7zq9c.jpg

Factor and solve the quadratic equation below, link them to the table above to complete the code in the four boxes at the bottom

Let's solve the quadratic equations one by one, factor them, and then match the solutions to the table provided to complete the code. I'll go through each equation and provide the solutions.

### 1. \( x^2 + x - 6 = 0 \)
Factor the quadratic:
\[
x^2 + x - 6 = (x - 2)(x + 3) = 0
\]
The solutions are:
\[
x = 2 \quad \text{or} \quad x = -3
\]
From the table, \( 2 \) corresponds to **R** and \( -3 \) corresponds to **D**.

### 2. \( x^2 + 3x + 2 = 0 \)
Factor the quadratic:
\[
x^2 + 3x + 2 = (x + 1)(x + 2) = 0
\]
The solutions are:
\[
x = -1 \quad \text{or} \quad x = -2
\]
From the table, \( -1 \) corresponds to **I** and \( -2 \) corresponds to **H**.

### 3. \( x^2 - x - 6 = 0 \)
Factor the quadratic:
\[
x^2 - x - 6 = (x - 3)(x + 2) = 0
\]
The solutions are:
\[
x = 3 \quad \text{or} \quad x = -2
\]
From the table, \( 3 \) corresponds to **F** and \( -2 \) corresponds to **H**.

### 4. \( x^2 - 3x + 2 = 0 \)
Factor the quadratic:
\[
x^2 - 3x + 2 = (x - 1)(x - 2) = 0
\]
The solutions are:
\[
x = 1 \quad \text{or} \quad x = 2
\]
From the table, \( 1 \) corresponds to **G** and \( 2 \) corresponds to **R**.

### 5. \( x^2 + 5x + 6 = 0 \)
Factor the quadratic:
\[
x^2 + 5x + 6 = (x + 2)(x + 3) = 0
\]
The solutions are:
\[
x = -2 \quad \text{or} \quad x = -3
\]
From the table, \( -2 \) corresponds to **H** and \( -3 \) corresponds to **D**.

### 6. \( x^2 - 7x + 12 = 0 \)
Factor the quadratic:
\[
x^2 - 7x + 12 = (x - 3)(x - 4) = 0
\]
The solutions are:
\[
x = 3 \quad \text{or} \quad x = 4
\]
From the table, \( 3 \) corresponds to **F** and \( 4 \) corresponds to **E**.

### 7. \( x^2 - 4x + 3 = 0 \)
Factor the quadratic:
\[
x^2 - 4x + 3 = (x - 1)(x - 3) = 0
\]
The solutions are:
\[
x = 1 \quad \text{or} \quad x = 3
\]
From the table, \( 1 \) corresponds to **G** and \( 3 \) corresponds to **F**.

### 8. \( x^2 - 9x + 18 = 0 \)
Factor the quadratic:
\[
x^2 - 9x + 18 = (x - 3)(x - 6) = 0
\]
The solutions are:
\[
x = 3 \quad \text{or} \quad x = 6
\]
From the table, \( 3 \) corresponds to **F** and \( 6 \) corresponds to **Q**.

### 9. \( x^2 + x - 56 = 0 \)
Factor the quadratic:
\[
x^2 + x - 56 = (x - 7)(x + 8) = 0
\]
The solutions are:
\[
x = 7 \quad \text{or} \quad x = -8
\]
From the table, \( 7 \) corresponds to **S** and \( -8 \) corresponds to **V**.

### 10. \( x^2 + 2x - 35 = 0 \)
Factor the quadratic:
\[
x^2 + 2x - 35 = (x - 5)(x + 7) = 0
\]
The solutions are:
\[
x = 5 \quad \text{or} \quad x = -7
\]
From the table, \( 5 \) corresponds to **K** and \( -7 \) corresponds to **T**.

### 11. \( x^2 - 6x - 27 = 0 \)
Factor the quadratic:
\[
x^2 - 6x - 27 = (x - 9)(x + 3) = 0
\]
The solutions are:
\[
x = 9 \quad \text{or} \quad x = -3
\]
From the table, \( 9 \) corresponds to **O** and \( -3 \) corresponds to **D**.

---

To complete the code at the bottom of the page, we need to use these results and the corresponding letters from the table.

Do you want me to help you fill in the boxes and verify the final code?

Factor and solve the quadratic equation below, link them to the table above to complete the code in the four boxes at the bottom.

Solve and factor quadratic equations to crack the code! This engaging activity challenges students to solve equations, match solutions to letters, and complete the final code. Includes practice on key algebraic concepts such as factoring quadratics and the zero product property. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation