Algebra factoring practice worksheet with 50 problems to factor expressions in the form A(x + B).

Let's solve the factorization problems in the worksheet. The task is to factorize each expression in the form $ A(x + B) $, where $ A $ is the greatest common factor (GCF) of the terms, and $ B $ is a constant.

We'll go through each problem step-by-step, identifying the GCF of the two terms and factoring it out.

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Step-by-step Solutions

#### 1) $ 9x + 18 $
- GCF of 9 and 18 is 9
- $ 9x + 18 = 9(x + 2) $

#### 2) $ 7x + 49 $
- GCF of 7 and 49 is 7
- $ 7x + 49 = 7(x + 7) $

#### 3) $ 3x + 9 $
- GCF of 3 and 9 is 3
- $ 3x + 9 = 3(x + 3) $

#### 4) $ 7x + 35 $
- GCF of 7 and 35 is 7
- $ 7x + 35 = 7(x + 5) $

#### 5) $ 5x + 35 $
- GCF of 5 and 35 is 5
- $ 5x + 35 = 5(x + 7) $

#### 6) $ 6x + 48 $
- GCF of 6 and 48 is 6
- $ 6x + 48 = 6(x + 8) $

#### 7) $ 7x + 28 $
- GCF of 7 and 28 is 7
- $ 7x + 28 = 7(x + 4) $

#### 8) $ 6x + 54 $
- GCF of 6 and 54 is 6
- $ 6x + 54 = 6(x + 9) $

#### 9) $ 4x + 24 $
- GCF of 4 and 24 is 4
- $ 4x + 24 = 4(x + 6) $

#### 10) $ 8x + 16 $
- GCF of 8 and 16 is 8
- $ 8x + 16 = 8(x + 2) $

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#### 21) $ 9x + 36 $
- GCF: 9 → $ 9(x + 4) $

#### 22) $ 8x + 72 $
- GCF: 8 → $ 8(x + 9) $

#### 23) $ 3x + 24 $
- GCF: 3 → $ 3(x + 8) $

#### 24) $ 4x + 8 $
- GCF: 4 → $ 4(x + 2) $

#### 25) $ 5x + 10 $
- GCF: 5 → $ 5(x + 2) $

#### 26) $ 8x + 40 $
- GCF: 8 → $ 8(x + 5) $

#### 27) $ 4x + 36 $
- GCF: 4 → $ 4(x + 9) $

#### 28) $ 2x + 16 $
- GCF: 2 → $ 2(x + 8) $

#### 29) $ 6x + 36 $
- GCF: 6 → $ 6(x + 6) $

#### 30) $ 2x + 8 $
- GCF: 2 → $ 2(x + 4) $

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#### 41) $ 5x + 25 $
- GCF: 5 → $ 5(x + 5) $

#### 42) $ 9x + 72 $
- GCF: 9 → $ 9(x + 8) $

#### 43) $ 2x + 4 $
- GCF: 2 → $ 2(x + 2) $

#### 44) $ 7x + 14 $
- GCF: 7 → $ 7(x + 2) $

#### 45) $ 2x + 14 $
- GCF: 2 → $ 2(x + 7) $

#### 46) $ 8x + 48 $
- GCF: 8 → $ 8(x + 6) $

#### 47) $ 4x + 16 $
- GCF: 4 → $ 4(x + 4) $

#### 48) $ 5x + 30 $
- GCF: 5 → $ 5(x + 6) $

#### 49) $ 4x + 32 $
- GCF: 4 → $ 4(x + 8) $

#### 50) $ 2x + 10 $
- GCF: 2 → $ 2(x + 5) $

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✔ Final Answer List:

| Problem | Factored Form |
|--------|----------------|
| 1) | $ 9(x + 2) $ |
| 2) | $ 7(x + 7) $ |
| 3) | $ 3(x + 3) $ |
| 4) | $ 7(x + 5) $ |
| 5) | $ 5(x + 7) $ |
| 6) | $ 6(x + 8) $ |
| 7) | $ 7(x + 4) $ |
| 8) | $ 6(x + 9) $ |
| 9) | $ 4(x + 6) $ |
| 10) | $ 8(x + 2) $ |
| 21) | $ 9(x + 4) $ |
| 22) | $ 8(x + 9) $ |
| 23) | $ 3(x + 8) $ |
| 24) | $ 4(x + 2) $ |
| 25) | $ 5(x + 2) $ |
| 26) | $ 8(x + 5) $ |
| 27) | $ 4(x + 9) $ |
| 28) | $ 2(x + 8) $ |
| 29) | $ 6(x + 6) $ |
| 30) | $ 2(x + 4) $ |
| 41) | $ 5(x + 5) $ |
| 42) | $ 9(x + 8) $ |
| 43) | $ 2(x + 2) $ |
| 44) | $ 7(x + 2) $ |
| 45) | $ 2(x + 7) $ |
| 46) | $ 8(x + 6) $ |
| 47) | $ 4(x + 4) $ |
| 48) | $ 5(x + 6) $ |
| 49) | $ 4(x + 8) $ |
| 50) | $ 2(x + 5) $ |

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🔍 Explanation:

To factor expressions like $ ax + b $ into $ A(x + B) $:
1. Find the greatest common factor (GCF) of the coefficients.
2. Factor that GCF out of both terms.
3. Write the result as $ \text{GCF}(x + \frac{b}{\text{GCF}}) $.

For example:
- $ 6x + 48 $: GCF = 6 → $ 6(x + 8) $ because $ 48 ÷ 6 = 8 $

This method works for all these linear binomials.

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