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Write a polynomial function of least degree with zeros -1, -7, and -2. Write your answer using the variable...

Write a polynomial function of least degree with zeros -1, -7, and -2.
Write your answer using the variable x and in standard form with a leading coefficient of 1.
f(x) =

Answer

f(x) = (x + 1)(x + 7)(x + 2)

Expanding this, we get:

  1. First, multiply (x + 1) and (x + 7):
  2. (x + 1)(x + 7) = x^2 + 7x + x + 7 = x^2 + 8x + 7

  3. Then, multiply the result by (x + 2):
  4. (x^2 + 8x + 7)(x + 2) = x^3 + 2x^2 + 8x^2 + 16x + 7x + 14 = x^3 + 10x^2 + 23x + 14

    So, the polynomial function is:

    f(x) = x^3 + 10x^2 + 23x + 14

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