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Answer :
To factor the expression [tex]\(-9 + 45x^3\)[/tex] completely, let's follow these steps:
1. Identify the Greatest Common Factor (GCF):
- Start by finding the greatest common factor of the numerical coefficients, which are [tex]\(-9\)[/tex] and [tex]\(45\)[/tex].
- The GCF of 9 and 45 is 9. Notice that [tex]\(-9\)[/tex] and [tex]\(45\)[/tex] are divisible by 9.
- Thus, the GCF is actually [tex]\(-9\)[/tex], considering both terms.
2. Factor out the GCF:
- Divide each term of the expression by [tex]\(-9\)[/tex].
- [tex]\(-9 \div -9 = 1\)[/tex]
- [tex]\(45x^3 \div -9 = -5x^3\)[/tex]
3. Rewrite the expression:
- After factoring out [tex]\(-9\)[/tex], the expression becomes:
[tex]\(-9(1 - 5x^3)\)[/tex].
4. Result:
- The expression is now factored completely as [tex]\(-9(1 - 5x^3)\)[/tex].
This is the fully factored form of the expression [tex]\(-9 + 45x^3\)[/tex].
1. Identify the Greatest Common Factor (GCF):
- Start by finding the greatest common factor of the numerical coefficients, which are [tex]\(-9\)[/tex] and [tex]\(45\)[/tex].
- The GCF of 9 and 45 is 9. Notice that [tex]\(-9\)[/tex] and [tex]\(45\)[/tex] are divisible by 9.
- Thus, the GCF is actually [tex]\(-9\)[/tex], considering both terms.
2. Factor out the GCF:
- Divide each term of the expression by [tex]\(-9\)[/tex].
- [tex]\(-9 \div -9 = 1\)[/tex]
- [tex]\(45x^3 \div -9 = -5x^3\)[/tex]
3. Rewrite the expression:
- After factoring out [tex]\(-9\)[/tex], the expression becomes:
[tex]\(-9(1 - 5x^3)\)[/tex].
4. Result:
- The expression is now factored completely as [tex]\(-9(1 - 5x^3)\)[/tex].
This is the fully factored form of the expression [tex]\(-9 + 45x^3\)[/tex].
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