Question

Expression: -50x⁷+25x
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: \(25x(-2x^6 + 1)\)