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Answer :
Final Answer:
The greatest common factor (GCF) of the polynomial 12x^(7)y^(3) - 20x^(6)y^(5) + 4x^(4)y^(6) is 4x^(4)y^(3).
Explanation:
To factor out the greatest common factor (GCF) from the polynomial 12x^(7)y^(3) - 20x^(6)y^(5) + 4x^(4)y^(6), we need to find the highest power of x and y that can be factored out from each term.
First, let's consider the x terms. The highest power of x that can be factored out from all the terms is x^(4).
Next, for the y terms, the highest power of y that can be factored out from all the terms is y^(3).
Now, we can factor out the GCF from each term:
12x^(7)y^(3) = 4x^(4)y^(3) * 3x^(3)
-20x^(6)y^(5) = 4x^(4)y^(3) * (-5x^(2)y^(2))
4x^(4)y^(6) = 4x^(4)y^(3) * y^(3)
As you can see, the GCF in all three terms is 4x^(4)y^(3). So, we can factor it out:
4x^(4)y^(3) * (3x^(3) - 5x^(2)y^(2) + y^(3))
This is the factored form of the given polynomial.
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