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Answer :
Factoring out the GCF, the polynomial's factored form is 28x²+16x⁵-20x⁶+12 = 4x²(7 + 4x³ - 5x⁴ + 3).
To factor out the greatest common factor (GCF) from the polynomial 28x² + 16x⁵ - 20x⁶ + 12, follow these steps:
- Identify the GCF of the coefficients: The coefficients are 28, 16, -20, and 12. The GCF of these numbers is 4.
- Determine the smallest power of x present in each term: The terms are 28x², 16x⁵, -20x⁶, and 12. The smallest power of x present is x² because 12 can be considered as 12x⁰.
- Combine the GCF of the coefficients and the smallest power of x to get the overall GCF: The GCF is 4x².
- Factor out the GCF from each term of the polynomial:
4x²(7 + 4x³ - 5x⁴ + 3)
Therefore, the factored form of the polynomial 28x² + 16x⁵ - 20x⁶ + 12 is 4x²(7 + 4x³ - 5x⁴ + 3).
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