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.
[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.
