Answer :

To factor out the greatest common factor (GCF) from the polynomial [tex]\(63x^4 + 81x^3 - 45x^5 + 18\)[/tex], let's go through the steps:

1. Identify the GCF of the coefficients: Look at the numerical coefficients, which are 63, 81, 45, and 18. We need to find the greatest common factor of these numbers.

- List the factors:
- 63: 1, 3, 7, 9, 21, 63
- 81: 1, 3, 9, 27, 81
- 45: 1, 3, 5, 9, 15, 45
- 18: 1, 2, 3, 6, 9, 18

- The greatest factor common to all the numbers is 9.

2. Factor 9 out from the polynomial: Now that we've identified the GCF as 9, we'll factor it out from each term of the polynomial.

- [tex]\(63x^4\)[/tex] becomes [tex]\(9 \times 7x^4\)[/tex]
- [tex]\(81x^3\)[/tex] becomes [tex]\(9 \times 9x^3\)[/tex]
- [tex]\(-45x^5\)[/tex] becomes [tex]\(9 \times (-5x^5)\)[/tex]
- [tex]\(18\)[/tex] becomes [tex]\(9 \times 2\)[/tex]

3. Write the factored expression: After factoring out 9 from each term, the polynomial becomes:

[tex]\[
9(7x^4 + 9x^3 - 5x^5 + 2)
\][/tex]

So, the factored form of [tex]\(63x^4 + 81x^3 - 45x^5 + 18\)[/tex] by taking out the GCF is [tex]\(9(7x^4 + 9x^3 - 5x^5 + 2)\)[/tex].

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