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Answer :
The polynomial 12x⁴y⁵ + 16x²y - 20x³y³ can be factored by taking out the greatest common factor (GCF) as 4x²y.
To factor the polynomial by taking out the GCF, we identify the highest common power of each variable, x and y, in each term. In this case, the highest common power of x is x² and the highest common power of y is y. So, the GCF is 4x²y. We then divide each term of the polynomial by this GCF. Dividing each term by 4x²y, we get: (12x⁴y⁵ ÷ 4x²y) + (16x²y ÷ 4x²y) - (20x³y³ ÷ 4x²y) = 3xy⁴ + 4 - 5xy². Thus, the factored form of the polynomial is 4x²y(3xy⁴ + 4 - 5xy²).
The given statement "Factor the polynomial by taking out the GCF: 12x⁴y⁵ + 16x²y - 20x³y³" is true because the process of factoring out the GCF involves finding the highest common factors of all terms and dividing each term by it. In this case, the GCF is 4x²y, which when divided out, leaves us with the factored polynomial 4x²y(3xy⁴ + 4 - 5xy²).
Correct option: Option A
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