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Which polynomial function f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3? f(x) = 3(x 5)(x 4)(x – 2)(x – 9) f(x) = 3(x – 5)(x – 4)(x 2)(x 9) f(x) = (x 5)(x 5)(x 5)(x 4)(x – 2)(x – 9) f(x) = (x – 5)(x – 5)(x – 5)(x – 4)(x 2)(x 9)

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MrRoyal

The equation of the polynomial function is f(x) = (x + 4)(x -2)(x -9)(x + 2)(x + 2)(x + 2)

How to determine the polynomial function?

The given parameters are:

  • Leading coefficient, n = 1
  • Root = -4; Multiplicity = 1
  • Root = 2; Multiplicity = 1
  • Root = 9; Multiplicity = 1
  • Root = -5; Multiplicity = 3

The polynomial function is represented as:

f(x) = n * (x - root)^multiplicity

So, we have:

f(x) = 1 *(x + 4)^1 * (x -2)^1 * (x -9)^1 * (x + 2)^3

This gives

f(x) = (x + 4)(x -2)(x -9)(x + 2)(x + 2)(x + 2)

Hence, the equation of the polynomial function is f(x) = (x + 4)(x -2)(x -9)(x + 2)(x + 2)(x + 2)

Read more about polynomial functions at:

https://brainly.com/question/2833285

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