Answer :
Final answer:
The factors of the polynomial x^(3)-5x^(2)+9x-45 are (x-5) and (x^(2)+9).
Explanation:
To find the factors of the polynomial x^(3)-5x^(2)+9x-45, we can use factoring by grouping or synthetic division. Let's use factoring by grouping:
- Group the terms with common factors. In this case, we can group the first two terms and the last two terms:
(x^(3)-5x^(2)) + (9x-45) - Factor out the common factors from each group:
x^(2)(x-5) + 9(x-5) - Notice that we now have a common factor of (x-5). Factor it out:
(x-5)(x^(2)+9)
Therefore, the factors of the polynomial x^(3)-5x^(2)+9x-45 are (x-5) and (x^(2)+9).
Learn more about finding factors of a polynomial here:
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