Answer :
To factor out the GCF from the polynomial 63x⁷ + 81x⁸ - 45x⁶ + 18, identify the highest power of x in each term and the largest number dividing each coefficient, which is 9x⁶. The factored form of the polynomial is 9x⁶(7x + 9x² - 5 + 2).
The question concerns factoring a polynomial to find the Greatest Common Factor (GCF). To factor out the GCF from a polynomial, we look for the highest power of x that is present in each term and the largest number that divides each of the coefficients. For the polynomial 63x⁷ + 81x⁸ - 45x⁶ + 18, the GCF is 9x⁶. We divide each term of the polynomial by the GCF to factor it out:
- 63x⁷ divided by 9x⁶ is 7x
- 81x⁸ divided by 9x⁶ is 9x²
- -45x⁶ divided by 9x⁶ is -5
- 18 has no x terms, so it remains 18, which is divisible by 9
After factoring out the GCF, the factored form of the polynomial is:
9x⁶(7x + 9x² - 5 + 2)
