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Use the given zero to find the remaining zeros of the polynomial function.

1. [tex]f(x) = x^4 - 7x^3 + 14x^2 - 38x - 60[/tex]; zero: [tex]1 + 3i[/tex]

2. [tex]g(x) = 2x^5 - 3x^4 - 5x^3 - 15x^2 - 207x + 108[/tex]; zero: [tex]3i[/tex]

Answer :

Final answer:

The remaining zeros of the polynomial function can be found by using the given zero and its conjugate.

Explanation:

To find the remaining zeros of the polynomial function, we need to use the given zero and its conjugate. Since the given zero is 1+3i, the conjugate is 1-3i. Therefore, the remaining zeros of the function are 1-3i and their conjugates.

Understanding polynomial functions involves examining their degree, leading coefficient, and zeros. Zeros are values of =0

P(x)=0, and they play a crucial role in determining the function's behavior. Polynomial factorization, breaking down a polynomial into its constituent linear and irreducible quadratic factors, helps identify its zeros.

Graphically, polynomial functions exhibit smooth curves with turning points, influenced by the degree and leading coefficient. These functions are foundational in algebra and calculus, applied in solving equations, analyzing functions, and modeling diverse real-world phenomena. The study of polynomial functions provides valuable insights into mathematical structures and their applications across various scientific disciplines.

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