Expression: -50x⁷+25x

Question

GCF: □
Factored form: □

Answer 1

To find the greatest common factor (GCF) and rewrite the expression in factored form, let's consider the expression:

\[ -50x^7 + 25x \]

Step 1: Identify the GCF of the coefficients and the variables.

1. The coefficients are -50 and 25. The GCF of -50 and 25 is 25.
2. The variable part has \(x^7\) and \(x^1\). The GCF is \(x^1 = x\).

Step 2: Combine the GCF.

The overall GCF is:

\[ 25x \]

Step 3: Factor out the GCF from the expression.

Now we can factor out \(25x\):

\[ -50x^7 + 25x = 25x(-2x^6 + 1) \]

So, we have:

GCF: \(25x\)

Factored form: \(25x(-2x^6 + 1)\)

Final Answer:

• GCF: \(25x\)
• Factored form: \(25x(-2x^6 + 1)\)