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].
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].
