To factor the expression \( 24x^4 + 56x^3 \) completely, we can follow these steps:
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Find the greatest common factor (GCF) of the coefficients (24 and 56) and the variable part (\(x^4\) and \(x^3\)):
- The GCF of 24 and 56 is 8.
- The GCF of \(x^4\) and \(x^3\) is \(x^3\).
Therefore, the overall GCF is \(8x^3\).
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Factor out the GCF:
\[ 24x^4 + 56x^3 = 8x^3(3x + 7) \]
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Check if \(3x + 7\) can be factored further:
The expression \(3x + 7\) is a linear polynomial and cannot be factored further.
Thus, the completely factored form of the expression \(24x^4 + 56x^3\) is:
\[ \boxed{8x^3(3x + 7)} \]
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