College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Factor the GCF out of the polynomial below:

\[ 28x^6 + 8x^4 + 12x^3 \]

Answer :

Let's factor out the greatest common factor (GCF) from the given polynomial:

[tex]\[ 28x^6 + 8x^4 + 12x^3 \][/tex]

### Step-by-Step Solution:

1. Identify the coefficients of each term:
- The coefficient of [tex]\(x^6\)[/tex] is 28.
- The coefficient of [tex]\(x^4\)[/tex] is 8.
- The coefficient of [tex]\(x^3\)[/tex] is 12.

2. Determine the GCF of the coefficients:
- The GCF of 28, 8, and 12 is 4.

3. Factor the GCF out of each term:
- [tex]\[ 28x^6 = 4 \cdot 7x^6 \][/tex]
- [tex]\[ 8x^4 = 4 \cdot 2x^4 \][/tex]
- [tex]\[ 12x^3 = 4 \cdot 3x^3 \][/tex]

4. Write the polynomial with the GCF factored out:
- [tex]\[ 28x^6 + 8x^4 + 12x^3 = 4(7x^6 + 2x^4 + 3x^3) \][/tex]

So, the polynomial factored by its greatest common factor (GCF) is:

[tex]\[ 4(7x^6 + 2x^4 + 3x^3) \][/tex]

This is the final factored form of the given polynomial.