To factor out the greatest common factor (GCF) from the polynomial \( 44b^5 + 2b^4 \), we first determine the GCF of the coefficients and the variable parts.
- Coefficients: The coefficients are \( 44 \) and \( 2 \). The GCF of \( 44 \) and \( 2 \) is \( 2 \).
- Variable parts: The variable parts are \( b^5 \) and \( b^4 \). The GCF of \( b^5 \) and \( b^4 \) is \( b^4 \) (the lowest power of \( b \)).
Now we can combine these to find the overall GCF:
\[ \text{GCF} = 2b^4 \]
Next, we factor \( 2b^4 \) out of each term of the polynomial:
\[ 44b^5 + 2b^4 = 2b^4(22b + 1) \]
Thus, the factored form is:
\[ \boxed{2b^4(22b + 1)} \]
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