Answer :

To factor out the Greatest Common Factor (GCF) from the polynomial [tex]\(8x^5 + 16x^9 - 12x^4 + 28\)[/tex], let's follow these steps:

1. Identify the GCF of the Coefficients:
- Look at the coefficients of each term: 8, 16, -12, and 28.
- Find the greatest common factor of these numbers.
- The factors of each number are:
- 8: 1, 2, 4, 8
- 16: 1, 2, 4, 8, 16
- -12: 1, 2, 3, 4, 6, 12
- 28: 1, 2, 4, 7, 14, 28
- The largest number that divides all of these is 4.

2. Factor out the GCF from the Polynomial:
- We factor 4 out of each term of the polynomial:
- [tex]\(8x^5 \div 4 = 2x^5\)[/tex]
- [tex]\(16x^9 \div 4 = 4x^9\)[/tex]
- [tex]\(-12x^4 \div 4 = -3x^4\)[/tex]
- [tex]\(28 \div 4 = 7\)[/tex]

3. Write the Factored Expression:
- After factoring out the GCF, the polynomial becomes:
[tex]\[
4(2x^5 + 4x^9 - 3x^4 + 7)
\][/tex]

So, the expression with the GCF factored out is [tex]\(4(2x^5 + 4x^9 - 3x^4 + 7)\)[/tex].

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