5-4 Factoring Linear Expressions WS1 worksheet - Free Printable

Problem: Factor each linear expression. If the expression cannot be factored, write "cannot be factored."

#### Step-by-Step Solution:

1. 17x + 34
- Find the greatest common factor (GCF) of 17 and 34.
- GCF(17, 34) = 17
- Factor out the GCF:
\[
17x + 34 = 17(x + 2)
\]
- Answer: \( 17(x + 2) \)

2. 10x + 25
- Find the GCF of 10 and 25.
- GCF(10, 25) = 5
- Factor out the GCF:
\[
10x + 25 = 5(2x + 5)
\]
- Answer: \( 5(2x + 5) \)

3. 30x + 18
- Find the GCF of 30 and 18.
- GCF(30, 18) = 6
- Factor out the GCF:
\[
30x + 18 = 6(5x + 3)
\]
- Answer: \( 6(5x + 3) \)

4. 45x − 18
- Find the GCF of 45 and 18.
- GCF(45, 18) = 9
- Factor out the GCF:
\[
45x - 18 = 9(5x - 2)
\]
- Answer: \( 9(5x - 2) \)

5. 38x − 12
- Find the GCF of 38 and 12.
- GCF(38, 12) = 2
- Factor out the GCF:
\[
38x - 12 = 2(19x - 6)
\]
- Answer: \( 2(19x - 6) \)

6. 28x + 15
- Find the GCF of 28 and 15.
- GCF(28, 15) = 1
- Since the GCF is 1, the expression cannot be factored further.
- Answer: cannot be factored

7. 3x − 27
- Find the GCF of 3 and 27.
- GCF(3, 27) = 3
- Factor out the GCF:
\[
3x - 27 = 3(x - 9)
\]
- Answer: \( 3(x - 9) \)

8. 6x + 24
- Find the GCF of 6 and 24.
- GCF(6, 24) = 6
- Factor out the GCF:
\[
6x + 24 = 6(x + 4)
\]
- Answer: \( 6(x + 4) \)

9. 26x − 5
- Find the GCF of 26 and 5.
- GCF(26, 5) = 1
- Since the GCF is 1, the expression cannot be factored further.
- Answer: cannot be factored

10. 48x + 56
- Find the GCF of 48 and 56.
- GCF(48, 56) = 8
- Factor out the GCF:
\[
48x + 56 = 8(6x + 7)
\]
- Answer: \( 8(6x + 7) \)

11. 15x − 14
- Find the GCF of 15 and 14.
- GCF(15, 14) = 1
- Since the GCF is 1, the expression cannot be factored further.
- Answer: cannot be factored

12. 20x − 100
- Find the GCF of 20 and 100.
- GCF(20, 100) = 20
- Factor out the GCF:
\[
20x - 100 = 20(x - 5)
\]
- Answer: \( 20(x - 5) \)

13. 7x + 35
- Find the GCF of 7 and 35.
- GCF(7, 35) = 7
- Factor out the GCF:
\[
7x + 35 = 7(x + 5)
\]
- Answer: \( 7(x + 5) \)

14. 7x + 17
- Find the GCF of 7 and 17.
- GCF(7, 17) = 1
- Since the GCF is 1, the expression cannot be factored further.
- Answer: cannot be factored

15. 9x − 63
- Find the GCF of 9 and 63.
- GCF(9, 63) = 9
- Factor out the GCF:
\[
9x - 63 = 9(x - 7)
\]
- Answer: \( 9(x - 7) \)

16. 39x + 13
- Find the GCF of 39 and 13.
- GCF(39, 13) = 13
- Factor out the GCF:
\[
39x + 13 = 13(3x + 1)
\]
- Answer: \( 13(3x + 1) \)

17. 8x + 15
- Find the GCF of 8 and 15.
- GCF(8, 15) = 1
- Since the GCF is 1, the expression cannot be factored further.
- Answer: cannot be factored

18. 18x − 12
- Find the GCF of 18 and 12.
- GCF(18, 12) = 6
- Factor out the GCF:
\[
18x - 12 = 6(3x - 2)
\]
- Answer: \( 6(3x - 2) \)

19. 24x + 48
- Find the GCF of 24 and 48.
- GCF(24, 48) = 24
- Factor out the GCF:
\[
24x + 48 = 24(x + 2)
\]
- Answer: \( 24(x + 2) \)

20. 45x − 81
- Find the GCF of 45 and 81.
- GCF(45, 81) = 9
- Factor out the GCF:
\[
45x - 81 = 9(5x - 9)
\]
- Answer: \( 9(5x - 9) \)

21. The area of a rectangular sandbox is \( 5x + 40 \) feet. Factor \( 5x + 40 \) to find possible dimensions of the sandbox.
- Find the GCF of 5 and 40.
- GCF(5, 40) = 5
- Factor out the GCF:
\[
5x + 40 = 5(x + 8)
\]
- The factored form \( 5(x + 8) \) suggests that the dimensions of the sandbox could be \( 5 \) feet and \( x + 8 \) feet.
- Answer: \( 5(x + 8) \)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 17(x + 2) \\
2. & 5(2x + 5) \\
3. & 6(5x + 3) \\
4. & 9(5x - 2) \\
5. & 2(19x - 6) \\
6. & \text{cannot be factored} \\
7. & 3(x - 9) \\
8. & 6(x + 4) \\
9. & \text{cannot be factored} \\
10. & 8(6x + 7) \\
11. & \text{cannot be factored} \\
12. & 20(x - 5) \\
13. & 7(x + 5) \\
14. & \text{cannot be factored} \\
15. & 9(x - 7) \\
16. & 13(3x + 1) \\
17. & \text{cannot be factored} \\
18. & 6(3x - 2) \\
19. & 24(x + 2) \\
20. & 9(5x - 9) \\
21. & 5(x + 8)
\end{array}
}
\]