Question

Expression: -25x³+5x²
GCF: □
Factored Form: □

Answer 1

To factor the expression \(-25x^3 + 5x^2\), we first need to find the greatest common factor (GCF) of the two terms.

1. **Identify the coefficients and variables:**
- The coefficients are \(-25\) and \(5\).
- The variable part is \(x^3\) and \(x^2\).

2. **Find the GCF of the coefficients:**
- The GCF of \(-25\) and \(5\) is \(5\).

3. **Find the GCF of the variable parts:**
- The common variable is \(x\), and the lower power is \(x^2\).

4. **Combine the GCF of the coefficients and variable parts:**
- Therefore, the overall GCF is \(5x^2\).

5. **Factor out the GCF from the original expression:**
\[
-25x^3 + 5x^2 = 5x^2(-5x + 1)
\]

- **GCF:** \(5x^2\)
- **Factored Form:** \(5x^2(-5x + 1)\)

So, we can summarize:

- GCF: \(5x^2\)
- Factored Form: \(5x^2(-5x + 1)\)