Algebra Factorising A1 worksheet featuring 50 algebraic expressions to factor in the form A(x + B), with spaces for student details and scoring.

Problem Description:

The task is to factorize each given algebraic expression into the form \( A(x + B) \), where \( A \) and \( B \) are constants. This involves identifying the greatest common factor (GCF) of the terms in each expression and factoring it out.

Solution Approach:

1. Identify the GCF: For each expression, determine the greatest common factor of the coefficients and the variable terms.
2. Factor out the GCF: Rewrite the expression by factoring out the GCF, leaving the remaining terms inside a parenthesis.

Step-by-Step Solutions:

#### Section 1: Questions 1–10
1. 9x + 18
- GCF of 9 and 18 is 9.
- Factor out 9: \( 9(x + 2) \).
- Answer: \( 9(x + 2) \)

2. 7x + 49
- GCF of 7 and 49 is 7.
- Factor out 7: \( 7(x + 7) \).
- Answer: \( 7(x + 7) \)

3. 3x + 9
- GCF of 3 and 9 is 3.
- Factor out 3: \( 3(x + 3) \).
- Answer: \( 3(x + 3) \)

4. 7x + 35
- GCF of 7 and 35 is 7.
- Factor out 7: \( 7(x + 5) \).
- Answer: \( 7(x + 5) \)

5. 5x + 35
- GCF of 5 and 35 is 5.
- Factor out 5: \( 5(x + 7) \).
- Answer: \( 5(x + 7) \)

6. 6x + 48
- GCF of 6 and 48 is 6.
- Factor out 6: \( 6(x + 8) \).
- Answer: \( 6(x + 8) \)

7. 7x + 28
- GCF of 7 and 28 is 7.
- Factor out 7: \( 7(x + 4) \).
- Answer: \( 7(x + 4) \)

8. 6x + 54
- GCF of 6 and 54 is 6.
- Factor out 6: \( 6(x + 9) \).
- Answer: \( 6(x + 9) \)

9. 4x + 24
- GCF of 4 and 24 is 4.
- Factor out 4: \( 4(x + 6) \).
- Answer: \( 4(x + 6) \)

10. 8x + 16
- GCF of 8 and 16 is 8.
- Factor out 8: \( 8(x + 2) \).
- Answer: \( 8(x + 2) \)

#### Section 2: Questions 21–30
11. 9x + 36
- GCF of 9 and 36 is 9.
- Factor out 9: \( 9(x + 4) \).
- Answer: \( 9(x + 4) \)

12. 8x + 72
- GCF of 8 and 72 is 8.
- Factor out 8: \( 8(x + 9) \).
- Answer: \( 8(x + 9) \)

13. 3x + 24
- GCF of 3 and 24 is 3.
- Factor out 3: \( 3(x + 8) \).
- Answer: \( 3(x + 8) \)

14. 4x + 8
- GCF of 4 and 8 is 4.
- Factor out 4: \( 4(x + 2) \).
- Answer: \( 4(x + 2) \)

15. 5x + 10
- GCF of 5 and 10 is 5.
- Factor out 5: \( 5(x + 2) \).
- Answer: \( 5(x + 2) \)

16. 8x + 40
- GCF of 8 and 40 is 8.
- Factor out 8: \( 8(x + 5) \).
- Answer: \( 8(x + 5) \)

17. 4x + 36
- GCF of 4 and 36 is 4.
- Factor out 4: \( 4(x + 9) \).
- Answer: \( 4(x + 9) \)

18. 2x + 16
- GCF of 2 and 16 is 2.
- Factor out 2: \( 2(x + 8) \).
- Answer: \( 2(x + 8) \)

19. 6x + 36
- GCF of 6 and 36 is 6.
- Factor out 6: \( 6(x + 6) \).
- Answer: \( 6(x + 6) \)

20. 2x + 8
- GCF of 2 and 8 is 2.
- Factor out 2: \( 2(x + 4) \).
- Answer: \( 2(x + 4) \)

#### Section 3: Questions 41–50
21. 5x + 25
- GCF of 5 and 25 is 5.
- Factor out 5: \( 5(x + 5) \).
- Answer: \( 5(x + 5) \)

22. 9x + 72
- GCF of 9 and 72 is 9.
- Factor out 9: \( 9(x + 8) \).
- Answer: \( 9(x + 8) \)

23. 2x + 4
- GCF of 2 and 4 is 2.
- Factor out 2: \( 2(x + 2) \).
- Answer: \( 2(x + 2) \)

24. 7x + 14
- GCF of 7 and 14 is 7.
- Factor out 7: \( 7(x + 2) \).
- Answer: \( 7(x + 2) \)

25. 2x + 14
- GCF of 2 and 14 is 2.
- Factor out 2: \( 2(x + 7) \).
- Answer: \( 2(x + 7) \)

26. 8x + 48
- GCF of 8 and 48 is 8.
- Factor out 8: \( 8(x + 6) \).
- Answer: \( 8(x + 6) \)

27. 4x + 16
- GCF of 4 and 16 is 4.
- Factor out 4: \( 4(x + 4) \).
- Answer: \( 4(x + 4) \)

28. 5x + 30
- GCF of 5 and 30 is 5.
- Factor out 5: \( 5(x + 6) \).
- Answer: \( 5(x + 6) \)

29. 4x + 32
- GCF of 4 and 32 is 4.
- Factor out 4: \( 4(x + 8) \).
- Answer: \( 4(x + 8) \)

30. 2x + 10
- GCF of 2 and 10 is 2.
- Factor out 2: \( 2(x + 5) \).
- Answer: \( 2(x + 5) \)

Final Answer:

\[
\boxed{
\begin{array}{lll}
1) & 9(x + 2) & 21) & 9(x + 4) & 41) & 5(x + 5) \\
2) & 7(x + 7) & 22) & 8(x + 9) & 42) & 9(x + 8) \\
3) & 3(x + 3) & 23) & 3(x + 8) & 43) & 2(x + 2) \\
4) & 7(x + 5) & 24) & 4(x + 2) & 44) & 7(x + 2) \\
5) & 5(x + 7) & 25) & 5(x + 2) & 45) & 2(x + 7) \\
6) & 6(x + 8) & 26) & 8(x + 5) & 46) & 8(x + 6) \\
7) & 7(x + 4) & 27) & 4(x + 9) & 47) & 4(x + 4) \\
8) & 6(x + 9) & 28) & 2(x + 8) & 48) & 5(x + 6) \\
9) & 4(x + 6) & 29) & 6(x + 6) & 49) & 4(x + 8) \\
10) & 8(x + 2) & 30) & 2(x + 4) & 50) & 2(x + 5) \\
\end{array}
}
\]