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Answer :
To factor the expression [tex]\(-9 + 45x^3\)[/tex] completely, let's break it down step-by-step:
1. Identify a common factor: Look at the coefficients of the terms in the expression [tex]\(-9\)[/tex] and [tex]\(45x^3\)[/tex]. The greatest common factor (GCF) of 9 and 45 is 9.
2. Factor out the GCF: Extract this common factor from each term:
[tex]\[
-9 + 45x^3 = 9(-1 + 5x^3)
\][/tex]
3. Resulting expression: The expression is factored completely as [tex]\(9(5x^3 - 1)\)[/tex].
After factoring the expression [tex]\(-9 + 45x^3\)[/tex], we get the complete factorization as [tex]\(9(5x^3 - 1)\)[/tex]. There are no further factors that can be extracted, making this the final solution.
1. Identify a common factor: Look at the coefficients of the terms in the expression [tex]\(-9\)[/tex] and [tex]\(45x^3\)[/tex]. The greatest common factor (GCF) of 9 and 45 is 9.
2. Factor out the GCF: Extract this common factor from each term:
[tex]\[
-9 + 45x^3 = 9(-1 + 5x^3)
\][/tex]
3. Resulting expression: The expression is factored completely as [tex]\(9(5x^3 - 1)\)[/tex].
After factoring the expression [tex]\(-9 + 45x^3\)[/tex], we get the complete factorization as [tex]\(9(5x^3 - 1)\)[/tex]. There are no further factors that can be extracted, making this the final solution.
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