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Answer :
Final answer:
The complete factorization of the trinomial 5x^(4) - 45x^(2) + 90 is 5*(x^2-6)*(x^2-3). This is accomplished by first factoring out the greatest common factor of 5, then factoring the remaining trinomial.
Explanation:
The function is 5x^(4) - 45x^(2) + 90. The goal is to factor this trinomial completely. First, you can factor out the greatest common factor (GCF), which is 5. From doing this, you get: 5*(x^(4) - 9x^(2) +18). Notice that the expression inside the parenthesis is a trinomial that can be factored again. This can be factored as (x^2-6)(x^2-3). So, the completely factored trinomial is 5*(x^2-6)*(x^2-3).
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