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Answer :
To factor the expression [tex]\(45x^4 - 54x^2\)[/tex], let's follow these steps:
1. Find the Greatest Common Factor (GCF):
- The coefficients are 45 and 54. The greatest common factor of 45 and 54 is 9.
- Also, we have the common variable term [tex]\(x^2\)[/tex] in both terms.
2. Factor out the GCF:
- First, factor 9 from the coefficients and [tex]\(x^2\)[/tex] from the variable terms.
- This leaves us with: [tex]\(9x^2(5x^2 - 6)\)[/tex].
3. Simplify and check for further factoring:
- Inside the parentheses, [tex]\(5x^2 - 6\)[/tex] does not factor further, as it is already in its simplest form.
Thus, the completely factored form of the expression [tex]\(45x^4 - 54x^2\)[/tex] is:
[tex]\[9x^2(5x^2 - 6).\][/tex]
By doing this step-by-step process, we ensure that the expression is factored as much as possible, and the result is simplified.
1. Find the Greatest Common Factor (GCF):
- The coefficients are 45 and 54. The greatest common factor of 45 and 54 is 9.
- Also, we have the common variable term [tex]\(x^2\)[/tex] in both terms.
2. Factor out the GCF:
- First, factor 9 from the coefficients and [tex]\(x^2\)[/tex] from the variable terms.
- This leaves us with: [tex]\(9x^2(5x^2 - 6)\)[/tex].
3. Simplify and check for further factoring:
- Inside the parentheses, [tex]\(5x^2 - 6\)[/tex] does not factor further, as it is already in its simplest form.
Thus, the completely factored form of the expression [tex]\(45x^4 - 54x^2\)[/tex] is:
[tex]\[9x^2(5x^2 - 6).\][/tex]
By doing this step-by-step process, we ensure that the expression is factored as much as possible, and the result is simplified.
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