find the factors and coefficient of the expresson -12ab+3a(b^2)c?

Let's break down the expression \(-12ab + 3a(b^2)c\) to find its factors and coefficients.

### Step 1: Factorization
We can look for common terms to factor out:

1. Both terms contain \(a\), so \(a\) is a common factor.
2. The remaining terms in each part are \(-12b\) and \(3b^2c\), respectively. We can also factor out the greatest common divisor (GCD) of \(-12\) and \(3\), which is \(3\).

Thus, we factor the expression as:

\[
-12ab + 3a(b^2)c = 3a(-4b + b^2c)
\]

### Step 2: Coefficients
The coefficients are the numerical values that multiply the variables. From the original expression:

- The coefficient of the first term \(-12ab\) is \(-12\).
- The coefficient of the second term \(3a(b^2)c\) is \(3\).

### Final Answer:
- **Factors**: \(3a\) and \((-4b + b^2c)\)
- **Coefficients**: \(-12\) and \(3\)

Would you like further details on factorization or any specific part of this solution?

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Here are 5 related questions for further exploration:

1. How do you find the GCD of two numbers in factorization?
2. What is the difference between factoring an expression and expanding it?
3. Can you factor polynomials with more than two terms?
4. What are the rules for factoring when variables are present in all terms?
5. How can factoring be used to simplify solving equations?

**Tip**: Always check for both numerical and variable common factors when factoring expressions.

find the factors and coefficient of the expression -12ab + 3a(b^2)c?

Explore how to find the factors and coefficients of the algebraic expression -12ab + 3a(b^2)c. This detailed breakdown demonstrates factoring common terms and identifying coefficients using the distributive property and GCD. Suitable for students in Grades 8-10.

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