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Answer :
Final answer:
The Greatest Common Factor (GCF) of the polynomial 18x7 + 81x5 - 45x2 + 63 is 9x2. When factored out, the polynomial becomes: 9x2(2x5 + 9x3 - 5x + 7).
Explanation:
To factor out the GCF (Greatest Common Factor) from the polynomial 18x7 + 81x5 - 45x2 + 63, first, you need to determine the GCF for all the coefficients and the variables present in the terms. You should consider both the numerical and the variable parts.
The GCF of the numerical coefficients (18, 81, -45, and 63) is 9. The smallest power of x that occurs in all terms is x2.
Therefore, the GCF is 9x2.
To factor out this GCF, divide each term of the polynomial by 9x2.
The polynomial becomes: 9x2(2x5 + 9x3 - 5x + 7).
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