Answer :
To factor the expression [tex]\(6x^8 + 9x^7 + 33x^5\)[/tex] completely, follow these steps:
1. Identify the Greatest Common Factor (GCF):
- Look at all the terms: [tex]\(6x^8\)[/tex], [tex]\(9x^7\)[/tex], and [tex]\(33x^5\)[/tex].
- The coefficients are 6, 9, and 33. The greatest common factor of these numbers is 3.
- For the variable parts, pick the smallest power of [tex]\(x\)[/tex]: [tex]\(x^5\)[/tex].
- Therefore, the GCF is [tex]\(3x^5\)[/tex].
2. Factor out the GCF:
- Divide each term by the GCF [tex]\(3x^5\)[/tex]:
- [tex]\(6x^8 \div 3x^5 = 2x^3\)[/tex]
- [tex]\(9x^7 \div 3x^5 = 3x^2\)[/tex]
- [tex]\(33x^5 \div 3x^5 = 11\)[/tex]
- After factoring out, the expression inside the parentheses is [tex]\(2x^3 + 3x^2 + 11\)[/tex].
3. Write the factored expression:
- Combine the GCF with the simplified expression:
[tex]\[
6x^8 + 9x^7 + 33x^5 = 3x^5(2x^3 + 3x^2 + 11)
\][/tex]
This expression is now factored completely.
1. Identify the Greatest Common Factor (GCF):
- Look at all the terms: [tex]\(6x^8\)[/tex], [tex]\(9x^7\)[/tex], and [tex]\(33x^5\)[/tex].
- The coefficients are 6, 9, and 33. The greatest common factor of these numbers is 3.
- For the variable parts, pick the smallest power of [tex]\(x\)[/tex]: [tex]\(x^5\)[/tex].
- Therefore, the GCF is [tex]\(3x^5\)[/tex].
2. Factor out the GCF:
- Divide each term by the GCF [tex]\(3x^5\)[/tex]:
- [tex]\(6x^8 \div 3x^5 = 2x^3\)[/tex]
- [tex]\(9x^7 \div 3x^5 = 3x^2\)[/tex]
- [tex]\(33x^5 \div 3x^5 = 11\)[/tex]
- After factoring out, the expression inside the parentheses is [tex]\(2x^3 + 3x^2 + 11\)[/tex].
3. Write the factored expression:
- Combine the GCF with the simplified expression:
[tex]\[
6x^8 + 9x^7 + 33x^5 = 3x^5(2x^3 + 3x^2 + 11)
\][/tex]
This expression is now factored completely.
