Part 1: If the roots of a polynomial are a, b, and c, then the factors can be written in the form (x - a), (x - b), and (x - c). In this case, we have (x - 3), (x - [3 + i]), and (x - [3 - i]). The three factors are (x - 3)(x - 3 - i)(x - 3 + i).
Part 2: The two factors with complex terms are (x - 3 - i)(x - 3 + i), and multiplying these terms as a difference of two squares can give:
(x - 3)^2 - i^2 = x^2 - 6x + 9 - (-1) = x^2 - 6x + 10
Part 3: We now multiply (x^2 - 6x + 10) by the remaining factor of (x - 3). This results in the cubic expression:
(x^2 - 6x + 10)(x - 3)
= x^3 - 3x^2 - 6x^2 + 18x + 10x - 30
= x^3 - 9x^2 + 28x - 30
Step-by-step explanation:
it is true though because
4 x -3 = -12
and
-12 - 2 = -14
Answer:
You have not added the options, therefore, I cannot provide an exact answer. However, I can help you with the concept.
In any fraction, the denominator cannot be equal to zero because this would make the fraction undefined.
Excluded values are the values that would make the denominator equal to zero.
We are given that the excluded values are 2 and 5, this means that the factors of the denominator are (x-2) and (x-5)
This means that the denominator is x² - 7x + 10
Pick the fraction which has this denominator.
Hope this helps :)
Answer:
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Step-by-step explanation:
