Determine the greatest common factor (GCF) for each expression and write its factored form. Note: the standard convention is to express the GCF as a positive number. (4 points) # Expression GCF Factored Form 1 −25x^3+5x^2

Answer 1

To determine the greatest common factor (GCF) of the expression \(-25x^3 + 5x^2\), we need to follow these steps:

1. Identify the coefficients of each term. The coefficients are \(-25\) and \(5\). The GCF of \(-25\) and \(5\) is \(5\).

2. Identify the variable parts of the terms. The variable parts are \(x^3\) and \(x^2\). The GCF of \(x^3\) and \(x^2\) is \(x^2\) (since we take the lowest exponent).

3. Combine the GCFs:

   • From the coefficients: \(5\)
   • From the variable parts: \(x^2\)

   Thus, the overall GCF is \(5x^2\).

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

So, the GCF and the factored form of the expression are as follows:

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

Summary:

Expression: \(-25x^3 + 5x^2\)

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