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Answer :
The greatest common factor (GCF) of the given expression is 4x^4. Factoring out 4x^4 yields: 4x^4(2x^3 + 3x^2 + 11).
To factor the expression 8x^7 + 12x^6 + 44x^4 by pulling out the greatest common factor (GCF), we first need to identify the highest power of x that appears in each term. In this case, the highest power of x is 7 in the first term, 6 in the second term, and 4 in the third term.
1: Identify the GCF
The GCF is the largest term that can be factored out from all the terms. In this expression, the GCF is 4x^4.
2: Divide each term by the GCF
Divide each term of the original expression by the GCF:
8x^7 / (4x^4) = 2x^(7-4) = 2x^3
12x^6 / (4x^4) = 3x^(6-4) = 3x^2
44x^4 / (4x^4) = 11
3: Write the factored expression
Factor out the GCF from each term and write the factored expression:
4x^4(2x^3 + 3x^2 + 11)
This is the fully factored expression: 4x^4(2x^3 + 3x^2 + 11).
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