Factor each polynomial. Check your work by distributing. If a polynomial cannot be factored, write "prime" 15a^2b - 30

Let's factor the polynomial: \( 15a^2b - 30 \).

### Step 1: Identify the greatest common factor (GCF)
- The terms are \( 15a^2b \) and \( -30 \).
- The GCF of 15 and 30 is 15.
- Since both terms have no common variables, the GCF is just 15.

### Step 2: Factor out the GCF
Factor out 15 from both terms:

\[
15a^2b - 30 = 15(a^2b - 2)
\]

### Step 3: Check your work by distributing
Now, distribute the 15 back into the factored expression to check:

\[
15(a^2b - 2) = 15a^2b - 30
\]

This matches the original polynomial, so the factorization is correct.

### Final Answer:
The factored form is \( 15(a^2b - 2) \).

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Would you like more details or have any questions? Here are some related problems to further practice:

1. Factor \( 12x^3 - 18x^2 \).
2. Factor \( 20y^2 - 5y \).
3. Factor \( 25m^3 - 50m^2 \).
4. Factor \( 9p^2q - 27q \).
5. Factor \( 6x^2 + 12x + 18 \).

**Tip:** Always begin by factoring out the greatest common factor (GCF) before trying other methods.

Factor each polynomial. Check your work by distributing. If a polynomial cannot be factored, write 'prime' 15a^2b - 30

Learn how to factor the polynomial 15a^2b - 30 by identifying the greatest common factor (GCF) and applying the distributive property. This step-by-step solution is perfect for students in Grades 6-8 and covers essential algebraic concepts.

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