Question

Expression: 25w¹⁰+5w⁸-10w³
GCF: □
Factored form: □

Answer 1

To factor the expression \(25w^{10} + 5w^8 - 10w^3\), we first need to find the greatest common factor (GCF) of the coefficients and the variable parts.

1. **Co-efficients**: The GCF of the coefficients \(25\), \(5\), and \(-10\) is \(5\).

2. **Variable part**: The expression has \(w^{10}\), \(w^8\), and \(w^3\). The GCF of the variable parts is \(w^3\) (the smallest power of \(w\)).

Now let's combine these results to find the overall GCF:

\[
\text{GCF} = 5w^3
\]

Next, we factor the expression using the GCF:

\[
25w^{10} + 5w^8 - 10w^3 = 5w^3(5w^7 + w^5 - 2)
\]

Now we can write the factored form:

### Final Answers
- GCF: **\(5w^3\)**
- Factored form: **\(5w^3(5w^7 + w^5 - 2)\)**