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:

[tex]\[ 28x^{10} + 20x^9 + 4x^8 = \square \][/tex]

Answer :

To factor out the Greatest Common Factor (GCF) from the polynomial [tex]\(28x^{10} + 20x^9 + 4x^8\)[/tex], follow these steps:

1. Identify the coefficients:
The polynomial has the terms with coefficients 28, 20, and 4.

2. Find the GCF of the coefficients:
To find the GCF of 28, 20, and 4, list the factors of each number:
- Factors of 28: 1, 2, 4, 7, 14, 28
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 4: 1, 2, 4

The greatest factor common to all three numbers is 4.

3. Factor out the GCF from each term in the polynomial:
- Divide each coefficient by the GCF (4) and write the polynomial with the GCF factored out:
- For [tex]\(28x^{10}\)[/tex], divide 28 by 4 to get 7. This gives [tex]\(7x^{10}\)[/tex].
- For [tex]\(20x^9\)[/tex], divide 20 by 4 to get 5. This gives [tex]\(5x^9\)[/tex].
- For [tex]\(4x^8\)[/tex], divide 4 by 4 to get 1. This gives [tex]\(1x^8\)[/tex].

4. Write the expression with the GCF factored out:
[tex]\[
28x^{10} + 20x^9 + 4x^8 = 4(x^{10} + 7x^9 + 1x^8)
\][/tex]

So, the polynomial factored by its GCF is [tex]\(4(x^{10} + 7x^9 + 1x^8)\)[/tex].