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Answer :
Using the Factor Theorem, it is found that the linear factorization of the function is:
[tex]f(x) = \left(x + \frac{11}{3}\right)\left(x - \frac{7}{2}\right)(x - 1 - 3i)(x - 1 + 3i)[/tex]
Factor Theorem:
The Factor Theorem states that a polynomial function with roots has linear factorization given by:
[tex]f(x) = (x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
Using a calculator, the roots of the function [tex]f(x) = 6x^4 - 11x^3 - 19x^2 + 164x - 770) are given by: [tex]x_1 = -\frac{11}{3}, x_2 = \frac{7}{2}, x_3 = 1 + 3i, x_4 = 1 - 3i[/tex]
Hence, applying the Factor Theorem, considering the given roots, the linear factorization given by:
[tex]f(x) = a(x - x_1)(x - x_2)(x - x_3)(x - x_4)[/tex]
[tex]f(x) = \left(x + \frac{11}{3}\right)\left(x - \frac{7}{2}\right)(x - 1 - 3i)(x - 1 + 3i)[/tex]
You can learn more about the Factor Theorem at https://brainly.com/question/24380382
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