Answer :
Final Answer:
The expression equivalent to [tex]x^(3) - 5x^(2) + 5x - 25 is d) (x - 5)(x^(2) + 5)[/tex].
Explanation:
To find the expression equivalent to [tex]x^(3) - 5x^(2) + 5x - 25[/tex], we can factor it. First, we can factor out the greatest common factor, which is 1, giving us:
[tex]x^(3) - 5x^(2) + 5x - 25 = x^(2)(x - 5) + 5(x - 5)[/tex]
Now, we can see that both terms have a common factor of [tex](x - 5)[/tex]. We can factor this out:
[tex]x^(2)(x - 5) + 5(x - 5) = (x - 5)(x^(2) + 5)[/tex]
So, the equivalent expression is [tex](x - 5)(x^(2) + 5)[/tex], which corresponds to option d).
This factoring simplifies the given expression while preserving its equivalence.
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