Factoring Quadratics Area Model

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Area model diagram showing quadratic factorisation

📚 Part 1: Understanding the Area Model

1. Look at this area model for x² + 5x + 6. Which factored form is correct?

(x + 2)(x + 3)

(x + 1)(x + 6)

(x + 5)(x + 1)

(x + 4)(x + 2)

2. For the expression x² + 7x + 10, what two numbers multiply to give 10 AND add to give 7?

1 and 10

2 and 5

3 and 4

-1 and -10

3. Which parts make up the area model for any quadratic x² + bx + c? (Select all that apply)

x² term

Linear x terms

Constant term

Coefficient of x²

4. Complete this area model by filling in the missing dimensions:

If the area of a rectangle is x² + 6x + 8, and one dimension is (x + 2), then the other dimension is __________.

✏️ Part 2: Factorising with Area Models

5. Use the area model to factorise x² + 4x + 3. Show your working in the box below:

Factored form: ________________

6. Draw an area model for x² + 8x + 15 and find the factors:

The factors of 15 that add to 8 are: _____ and _____

Factored form: ________________

7. Explain in your own words how the area model helps you understand factorisation:

8. Challenge: If x² + 9x + 14 = (x + a)(x + b), find the values of a and b, then explain how you could check your answer:

a = _____ and b = _____

Check by: _________________________________

🎯 Part 3: Connecting Factors to Solutions

9. If x² + 6x + 5 = (x + 1)(x + 5), what are the solutions when x² + 6x + 5 = 0?

x = 1 and x = 5

x = -1 and x = -5

x = 1 and x = -5

x = -1 and x = 5

10. Extension: A rectangular garden has an area of (x² + 7x + 12) square metres. If the length is (x + 4) metres, what is the width? If x = 3, what are the actual dimensions?

Width = _____________ metres

When x = 3: Length = _____ m, Width = _____ m, Area = _____ m²

Factoring Quadratics Area Model

Factoring Quadratics Area Model

📚 Part 1: Understanding the Area Model

✏️ Part 2: Factorising with Area Models

🎯 Part 3: Connecting Factors to Solutions

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