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Answer :
Final answer:
The greatest common factor (GCF) for the given mathematical expression is 3x^(2)y³. We calculate this by looking for the highest number or variable that divides each term of the expression.
Explanation:
The goal is to find the greatest common factor (GCF) of the given polynomial expression 45x^(5)y^(7) + 33x^(3)y³ + 78x^(2)y^(4). GCF is the highest number or variable that divides each term of the expression.
The coefficients for the terms are 45, 33, and 78. The GCF of these numbers is 3. Next, look for the powers of x. Here they are 5, 3, and 2. The smallest power is 2, so x² is the GCF for the x part of the terms. For the y part, the powers are 7, 3, and 4. The smallest power is 3, so y³ is the GCF for the y part of the term.
Overall, the GCF of the given expression is 3x^(2)y³.
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