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12c2 - 2c

Question 6Select one:

2(6c - c)

2c(6c - 1)

c(12c - 2)

6c(2c - c)

We are given the expression \( 12c^2 - 2c \) and need to factor it.

### Step 1: Find the greatest common factor (GCF)
Both terms in the expression \( 12c^2 - 2c \) share a common factor of \( 2c \).

- The first term, \( 12c^2 \), can be factored as \( 2c(6c) \).
- The second term, \( -2c \), can be factored as \( 2c(-1) \).

### Step 2: Factor out the GCF
Factor out \( 2c \) from the expression:
\[
12c^2 - 2c = 2c(6c - 1)
\]

Thus, the factored form of \( 12c^2 - 2c \) is:
\[
2c(6c - 1)
\]

### Conclusion:
The correct answer is **2c(6c - 1)**.

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Would you like more details or have any questions?

Here are five related questions:
1. How do you determine the greatest common factor in a polynomial?
2. What are the steps to factor a quadratic expression?
3. How can you verify that the factored expression is correct?
4. Why is factoring important in solving quadratic equations?
5. Can all quadratic expressions be factored using integers?

**Tip:** Always look for the greatest common factor (GCF) first when factoring expressions—it simplifies the problem significantly.

Learn how to factor the polynomial 12c^2 - 2c by finding the greatest common factor (GCF). This step-by-step guide simplifies the problem and shows the correct factoring process, making it ideal for students in Grades 8-10.

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