Answer :
To factor the expression [tex]\(-9 + 45x^3\)[/tex] completely, follow these steps:
1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients: [tex]\(-9\)[/tex] and [tex]\(45\)[/tex].
- The greatest common factor of [tex]\(9\)[/tex] and [tex]\(45\)[/tex] is [tex]\(9\)[/tex].
2. Factor out the GCF:
- Divide each term in the expression by [tex]\(9\)[/tex].
- [tex]\(-9 \div 9 = -1\)[/tex]
- [tex]\(45x^3 \div 9 = 5x^3\)[/tex]
So, the expression becomes:
[tex]\[
9(-1 + 5x^3)
\][/tex]
3. Check if the expression inside the parentheses can be factored further:
- [tex]\(-1 + 5x^3\)[/tex] cannot be factored further with real numbers.
Therefore, the completely factored form of the expression [tex]\(-9 + 45x^3\)[/tex] is:
[tex]\[
9(-1 + 5x^3)
\][/tex]
1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients: [tex]\(-9\)[/tex] and [tex]\(45\)[/tex].
- The greatest common factor of [tex]\(9\)[/tex] and [tex]\(45\)[/tex] is [tex]\(9\)[/tex].
2. Factor out the GCF:
- Divide each term in the expression by [tex]\(9\)[/tex].
- [tex]\(-9 \div 9 = -1\)[/tex]
- [tex]\(45x^3 \div 9 = 5x^3\)[/tex]
So, the expression becomes:
[tex]\[
9(-1 + 5x^3)
\][/tex]
3. Check if the expression inside the parentheses can be factored further:
- [tex]\(-1 + 5x^3\)[/tex] cannot be factored further with real numbers.
Therefore, the completely factored form of the expression [tex]\(-9 + 45x^3\)[/tex] is:
[tex]\[
9(-1 + 5x^3)
\][/tex]
