Factoring expressions worksheet with algebraic problems for practice.

Let’s solve each expression by factoring. Factoring means finding the greatest common factor (GCF) of the terms and writing the expression as a product.

We’ll go one by one:

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16. 7x + 35
Both terms are divisible by 7.
7x ÷ 7 = x
35 ÷ 7 = 5
→ 7(x + 5)

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17. 8x + 24
Both terms divisible by 8.
8x ÷ 8 = x
24 ÷ 8 = 3
→ 8(x + 3)

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18. 4x + 35
Check GCF of 4 and 35 → factors of 4: 1,2,4; factors of 35: 1,5,7,35 → only common factor is 1.
So this cannot be factored further with integers.
→ Already simplified: 4x + 35

*(Note: Sometimes problems expect you to leave it if no common factor >1 exists.)*

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19. 3x + 15
Divisible by 3.
3x ÷ 3 = x
15 ÷ 3 = 5
→ 3(x + 5)

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20. 6x + 54
Divisible by 6.
6x ÷ 6 = x
54 ÷ 6 = 9
→ 6(x + 9)

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21. 10x + 100
Divisible by 10.
10x ÷ 10 = x
100 ÷ 10 = 10
→ 10(x + 10)

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22. 12x + 8
GCF of 12 and 8 is 4.
12x ÷ 4 = 3x
8 ÷ 4 = 2
→ 4(3x + 2)

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23. 22x + 55
GCF of 22 and 55 is 11.
22x ÷ 11 = 2x
55 ÷ 11 = 5
→ 11(2x + 5)

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24. 8x + 32x
Wait — both terms have “x”, so combine first? Actually, they’re like terms!
8x + 32x = 40x
But if we factor without combining:
GCF of 8 and 32 is 8, and both have x → factor out 8x
8x + 32x = 8x(1 + 4) = 8x(5) → but that’s just 40x.
Actually, better to combine first:
→ 40x
But if the problem wants factoring *before* combining:
Factor out 8x: 8x(1 + 4) = 8x·5 = 40x — same thing.
Alternatively, factor out 8: 8(x + 4x) = 8(5x) = 40x — still same.
Best answer: Since it’s two like terms, simplify first → 40x
But if forced to factor: 8x(1 + 4) or 8( x + 4x ) — not standard.
Actually, let’s check original: “8x + 32x” — yes, like terms. So simplest form is 40x. But maybe typo? Perhaps meant 8x + 32? Let me re-read image description... User wrote “24. 8x + 32x” — so yes, like terms.
→ Final: 40x
But wait — perhaps the intention was to factor even if like terms? Unusual. Maybe it's 8x + 32? Let me double-check user input: “24. 8x + 32x” — okay, so I’ll go with combining.
However, in factoring exercises, sometimes they give like terms to test if you notice. But typically, you’d combine first.
To be safe, I’ll factor out the GCF of coefficients and variable:
Coefficients: 8 and 32 → GCF=8; variables: x and x → so factor out 8x:
8x(1 + 4) = 8x * 5 = 40x — so factored form could be written as 8x(5), but that’s not useful.
I think best is to simplify: 40x

But let’s see other problems — all others are binomials with different terms. Maybe it’s a typo and should be 8x + 32? In many worksheets, #24 is often 8x+32. Given that, and since 8x+32x is unusual, I suspect it might be 8x + 32. But user wrote “32x”. I must follow what’s given.

Given: 8x + 32x = 40x → which is already simplified. No need to factor.
→ 40x

But to match format, perhaps write as 8x(1 + 4)? Not standard. I’ll go with simplified form.

Wait — another thought: maybe it’s 8x + 32y? But user said “32x”. I’ll proceed as written.

Final decision: Since it’s 8x + 32x, combine to 40x. So answer is 40x

But let’s move on and come back.

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25. 8y + 8y
Again, like terms! 8y + 8y = 16y
Or factor: 8y(1 + 1) = 8y*2 = 16y
→ 16y

Same issue as above. Probably intended to be different variables? But as written, combine.

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26. 36x + 9
GCF of 36 and 9 is 9.
36x ÷ 9 = 4x
9 ÷ 9 = 1
→ 9(4x + 1)

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27. 20z + 40z
Like terms again! 20z + 40z = 60z
Or factor: 20z(1 + 2) = 60z
→ 60z

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28. 35x + 60
GCF of 35 and 60. Factors: 35=5*7, 60=5*12 → GCF=5
35x ÷ 5 = 7x
60 ÷ 5 = 12
→ 5(7x + 12)

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29. 13x + 39
GCF of 13 and 39 is 13 (since 39=13*3)
13x ÷ 13 = x
39 ÷ 13 = 3
→ 13(x + 3)

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30. 28x + 42
GCF of 28 and 42. 28=2*2*7, 42=2*3*7 → GCF=14
28x ÷ 14 = 2x
42 ÷ 14 = 3
→ 14(2x + 3)

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Now, going back to the ones with like terms: #24, #25, #27.

In standard factoring exercises, if two terms are like terms, you combine them first. The purpose of factoring is to rewrite sums as products when there’s a common factor across unlike terms. For like terms, simplification comes first.

So:

- #24: 8x + 32x = 40x → final answer 40x
- #25: 8y + 8y = 16y → 16y
- #27: 20z + 40z = 60z → 60z

But let me verify if perhaps the original had typos. For example, #24 might be 8x + 32 (without x on second term). Similarly, #25 might be 8y + 8z, etc. But based on user input, I have to use what’s given.

User wrote:
“24. 8x + 32x”
“25. 8y + 8y”
“27. 20z + 40z”

So I’ll treat them as is.

However, in some contexts, they might want you to factor even if like terms — for example, factor out the coefficient and variable. But that would be redundant.

For consistency, I’ll provide the simplified form for those.

But let’s check #18: 4x + 35 — no common factor, so left as is.

Similarly, for like terms, after combining, they are monomials, so no factoring needed.

So final answers:

16. 7(x + 5)
17. 8(x + 3)
18. 4x + 35 (no common factor)
19. 3(x + 5)
20. 6(x + 9)
21. 10(x + 10)
22. 4(3x + 2)
23. 11(2x + 5)
24. 40x (since 8x + 32x = 40x)
25. 16y (8y + 8y = 16y)
26. 9(4x + 1)
27. 60z (20z + 40z = 60z)
28. 5(7x + 12)
29. 13(x + 3)
30. 14(2x + 3)

I think that’s correct.

Just to be thorough, let’s verify a couple:

#22: 4(3x + 2) = 12x + 8 ✓
#23: 11(2x + 5) = 22x + 55 ✓
#28: 5(7x + 12) = 35x + 60 ✓
#30: 14(2x + 3) = 28x + 42 ✓

And for like terms:
#24: 8x + 32x = 40x ✓
#25: 8y + 8y = 16y ✓
#27: 20z + 40z = 60z ✓

All good.

Final Answer:
16. 7(x + 5)
17. 8(x + 3)
18. 4x + 35
19. 3(x + 5)
20. 6(x + 9)
21. 10(x + 10)
22. 4(3x + 2)
23. 11(2x + 5)
24. 40x
25. 16y
26. 9(4x + 1)
27. 60z
28. 5(7x + 12)
29. 13(x + 3)
30. 14(2x + 3)