Respuesta :

Using the Factor Theorem, it is found that it is possible for a trinomial with a leading coefficient not equal to 1 have two identical factors, and an example is:

[tex]f(x) = 2(x - 1)^2(x - 2)[/tex]

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.

In this problem:

  • Leading coefficient of [tex]a = 2[/tex].
  • Identical factors at x = 1, hence [tex]x_1 = x_2 = 1[/tex].
  • A trinomial has three factors, hence for example another one at x = 3, hence [tex]x_3 = 3[/tex]

Then, the example of the trinomial is:

[tex]f(x) = 2(x - 1)^2(x - 2)[/tex]

You can learn more about the Factor Theorem at https://brainly.com/question/24380382

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