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Sagot :
Using the Factor Theorem, the second degree polynomial function that has a leading coefficient of –1 and root 4 with multiplicity 2 is given by:
f(x) = -x² + 8x - 16
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, we have that:
- The leading coefficient is of a = -1.
- There is a root of 4 with multiplicity 2, hence [tex]x_1 = x_2 = 4[/tex].
Thus, the polynomial is given by:
f(x) = -(x - 4)(x - 4)
f(x) = -(x² - 8x + 16)
f(x) = -x² + 8x - 16
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
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