Using the Factor Theorem, the polynomial function is given by:
f(x) = (x - 7)(x - 5)(x - 5)(x + 2), which means that the last option is correct.
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.
In this problem:
- The leading coefficient is of a = 1.
- The roots with multiplicity 1 are [tex]x_1 = -2, x_2 = 7[/tex].
- Since the root of 5 has multiplicity 2, [tex]x_3 = x_4 = 5[/tex].
Hence, the function is given by:
f(x) = (x - 7)(x - 5)(x - 5)(x + 2), which means that the last option is correct.
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
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