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Sagot :
Using the Factor Theorem, Andrew's error was at the application of the minus signal to the complex roots, and the polynomial of degree 3 is of f(x) = x³ - 7x² + 20x - 24.
What is the Factor Theorem?
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
For this problem, the roots are given as follows:
- [tex]x_1 = 3[/tex].
- [tex]x_2 = 2 + 2i[/tex].
- [tex]x_3 = 2 - 2i[/tex].
Hence the polynomial is given as follows, considering leading coefficient a = 1:
[tex]f(x) = (x - 3)(x - 2 - 2i)(x - 2 + 2i)[/tex]
His error was at the application of the minus signal to the complex roots.
Then:
f(x) = (x - 3)[(x - 2)² - (2i)²]
f(x) = (x - 3)(x² - 4x + 4 + 4)
f(x) = (x - 3)(x² - 4x + 8)
f(x) = x³ - 7x² + 20x - 24.
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
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