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Answer :
Final answer:
The largest possible common factor of the polynomial 45x⁶+18x⁵+27x⁴ is 9x⁴. After dividing each term by 9x⁴, the polynomial simplifies to 5x² + 2x + 3. Hence, the factored form of the polynomial is 9x⁴(5x² + 2x + 3).
Explanation:
The common factor of the given polynomial 45x⁶+18x⁵+27x⁴ is obtained through the process of factoring. This can be done by first identifying the greatest common factor (GCF) that could be divided evenly into all terms of the polynomial. The GCF of the coefficients (45, 18, 27) is 9. The smallest power of x in all terms is 4. Thus, the GCF is 9x⁴.
After we've found the GCF, we divide each term of the polynomial by the GCF. So, (45x⁶ ÷ 9x⁴) + (18x⁵ ÷ 9x⁴) + (27x⁴ ÷ 9x⁴) simplifies to 5x² + 2x + 3.
Therefore, the factored form of the polynomial is 9x⁴(5x² + 2x + 3).
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