Factors of `-5x^2 y^2 z` are

Options

A. `-5 xx x xx y xx z`
B. `-5 xx x^2 xx y xx z`
C. `-5 xx x xx x xx y xx y xx z`
D. `-5 xx x xx y xx z^2`

Answer

To find the factors of the expression \(-5x^2 y^2 z\), we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the components of the expression**:
The expression \(-5x^2 y^2 z\) consists of a coefficient \(-5\) and the variables \(x^2\), \(y^2\), and \(z\).

2. **Factor the coefficient**:
The coefficient \(-5\) can be expressed as \(-5\) itself.

3. **Factor the variable \(x^2\)**:
The term \(x^2\) can be factored as \(x \cdot x\).

4. **Factor the variable \(y^2\)**:
Similarly, the term \(y^2\) can be factored as \(y \cdot y\).

5. **Include the variable \(z\)**:
The variable \(z\) remains as it is since it is already in its simplest form.

6. **Combine all the factors**:
Putting all the factors together, we have:
\[ -5x^2y^2z = -5 \cdot x \cdot x \cdot y \cdot y \cdot z \]

7. **Final expression of factors**:
Therefore, the factors of the expression \(-5x^2y^2z\) are:
\[ -5, x, x, y, y, z \]

### Final Answer:
The factors of \(-5x^2y^2z\) are \(-5\), \(x\), \(x\), \(y\), \(y\), and \(z\).

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