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Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial. 30u^5–45u^3Asked by oliver
Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
44b^5+2b^4
44b^5+2b^4
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Answered by
GPT-4o mini
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.
1. **Coefficients**: The coefficients are \( 44 \) and \( 2 \). The GCF of \( 44 \) and \( 2 \) is \( 2 \).
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:
\[
\boxed{2b^4(22b + 1)}
\]
1. **Coefficients**: The coefficients are \( 44 \) and \( 2 \). The GCF of \( 44 \) and \( 2 \) is \( 2 \).
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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