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.
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Co-efficients: The GCF of the coefficients \(25\), \(5\), and \(-10\) is \(5\).
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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: \(5w^3(5w^7 + w^5 - 2)\)