Answer :
Sure! Let's factor out the greatest common factor (GCF) from the polynomial [tex]\(21x^6 + 15x^4 + 9x^3\)[/tex]. Here is the step-by-step solution:
1. Identify the coefficients of the polynomial, which are 21, 15, and 9.
2. Determine the GCF of these coefficients.
- The factors of 21 are 1, 3, 7, 21.
- The factors of 15 are 1, 3, 5, 15.
- The factors of 9 are 1, 3, 9.
- The common factor in all three sets is 3.
- Thus, the GCF of 21, 15, and 9 is 3.
3. Factor out the GCF from each term:
- For the term [tex]\(21x^6\)[/tex], factor out 3: [tex]\(21x^6 = 3 \cdot 7x^6\)[/tex].
- For the term [tex]\(15x^4\)[/tex], factor out 3: [tex]\(15x^4 = 3 \cdot 5x^4\)[/tex].
- For the term [tex]\(9x^3\)[/tex], factor out 3: [tex]\(9x^3 = 3 \cdot 3x^3\)[/tex].
4. Write the polynomial with the GCF factored out:
[tex]\[
21x^6 + 15x^4 + 9x^3 = 3(7x^6 + 5x^4 + 3x^3)
\][/tex]
So, the factored form of the polynomial [tex]\(21x^6 + 15x^4 + 9x^3\)[/tex] with the GCF factored out is [tex]\(3(7x^6 + 5x^4 + 3x^3)\)[/tex].
1. Identify the coefficients of the polynomial, which are 21, 15, and 9.
2. Determine the GCF of these coefficients.
- The factors of 21 are 1, 3, 7, 21.
- The factors of 15 are 1, 3, 5, 15.
- The factors of 9 are 1, 3, 9.
- The common factor in all three sets is 3.
- Thus, the GCF of 21, 15, and 9 is 3.
3. Factor out the GCF from each term:
- For the term [tex]\(21x^6\)[/tex], factor out 3: [tex]\(21x^6 = 3 \cdot 7x^6\)[/tex].
- For the term [tex]\(15x^4\)[/tex], factor out 3: [tex]\(15x^4 = 3 \cdot 5x^4\)[/tex].
- For the term [tex]\(9x^3\)[/tex], factor out 3: [tex]\(9x^3 = 3 \cdot 3x^3\)[/tex].
4. Write the polynomial with the GCF factored out:
[tex]\[
21x^6 + 15x^4 + 9x^3 = 3(7x^6 + 5x^4 + 3x^3)
\][/tex]
So, the factored form of the polynomial [tex]\(21x^6 + 15x^4 + 9x^3\)[/tex] with the GCF factored out is [tex]\(3(7x^6 + 5x^4 + 3x^3)\)[/tex].
