A polynomial in x whose zeros are -2, -1 and 3 is

  • A \(x^3 - 7x + 6\)
  • B \(x^3 + 7x - 6\)
  • C \(x^3 + 7x + 6\)
  • D \(x^3 - 7x - 6\)

The correct answer is D. \(x^3 - 7x - 6\)

If a polynomial has zeros at \(x = -2\), \(x = -1\), and \(x = 3\), then it can be written in factored form as \((x + 2)(x + 1)(x - 3)\). Multiplying these factors, we get:

\((x + 2)(x + 1)(x - 3) = (x^2 + 3x + 2)(x - 3)\)

\(= x^3 + 3x^2 + 2x - 3x^2 - 9x - 6\)

\(= x^3 - 7x - 6\)

So, a polynomial in x whose zeros are -2, -1 and 3 is \(x^3 - 7x - 6\).

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