Answer :

To factor the expression [tex]\(-9 + 45x^3\)[/tex] completely, follow these steps:

1. Identify the Greatest Common Factor (GCF):
- Look for the greatest common factor of the coefficients in the expression.
- The coefficients are [tex]\(-9\)[/tex] and [tex]\(45\)[/tex].
- The GCF of [tex]\(-9\)[/tex] and [tex]\(45\)[/tex] is [tex]\(9\)[/tex].

2. Factor out the GCF:
- Since the leading term in the expression is negative ([tex]\(-9\)[/tex]), we factor out [tex]\(-9\)[/tex] from the expression.
- Divide each term in the expression by [tex]\(-9\)[/tex].

3. Rewrite the Expression:
- When [tex]\(-9\)[/tex] is factored out, the expression becomes:
[tex]\[
-9 \left(\frac{-9}{-9} + \frac{45x^3}{-9} \right)
\][/tex]
- Simplifying inside the parentheses gives:
[tex]\[
-9 (1 - 5x^3)
\][/tex]

So, the completely factored expression is:

[tex]\[
-9(1 - 5x^3)
\][/tex]

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