Answer :
Consider the original expression:
[tex]$$45x^6 - 25x^2 - 25.$$[/tex]
Step 1. Factor Out the Greatest Common Factor (GCF):
Notice that each term in the expression has a factor of [tex]$5$[/tex]. Factor [tex]$5$[/tex] out:
[tex]$$45x^6 - 25x^2 - 25 = 5(9x^6 - 5x^2 - 5).$$[/tex]
Step 2. Examine the Expression Inside the Parentheses:
We now have:
[tex]$$5(9x^6 - 5x^2 - 5).$$[/tex]
At this stage, [tex]$9x^6 - 5x^2 - 5$[/tex] does not have any common factors among its terms that can be factored out further. In addition, there is no obvious factorization into lower-degree polynomials with integer coefficients.
Final Answer:
Thus, the factored form of the expression is:
[tex]$$\boxed{5(9x^6 - 5x^2 - 5)}.$$[/tex]
[tex]$$45x^6 - 25x^2 - 25.$$[/tex]
Step 1. Factor Out the Greatest Common Factor (GCF):
Notice that each term in the expression has a factor of [tex]$5$[/tex]. Factor [tex]$5$[/tex] out:
[tex]$$45x^6 - 25x^2 - 25 = 5(9x^6 - 5x^2 - 5).$$[/tex]
Step 2. Examine the Expression Inside the Parentheses:
We now have:
[tex]$$5(9x^6 - 5x^2 - 5).$$[/tex]
At this stage, [tex]$9x^6 - 5x^2 - 5$[/tex] does not have any common factors among its terms that can be factored out further. In addition, there is no obvious factorization into lower-degree polynomials with integer coefficients.
Final Answer:
Thus, the factored form of the expression is:
[tex]$$\boxed{5(9x^6 - 5x^2 - 5)}.$$[/tex]
