Write a polynomial of least degree with real coefficients and with the root 1–6𝑖.

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Recognize Property of Complex Roots: Recognize that if a polynomial has real coefficients and a complex root, then the complex conjugate of that root must also be a root of the polynomial. The complex conjugate of 1–6𝑖 is 1+6𝑖.Write Root Factors: Write the factors associated with the roots 1–6𝑖 and 1+6𝑖. The factors are (x - (1 - 6𝑖)) and (x - (1 + 6𝑖)).Multiply Factors: Multiply the two factors to obtain the polynomial. We have: (x - (1 - 6𝑖))(x - (1 + 6𝑖)) = (x - 1 + 6𝑖)(x - 1 - 6𝑖).Expand Using FOIL Method: Use the FOIL method to expand the product of the two binomials: (x - 1 + 6𝑖)(x - 1 - 6𝑖) = x^2 - x - 6𝑖x - x + 1 + 6𝑖 - 6𝑖x + 6𝑖 + 36𝑖^2.Simplify Expression: Simplify the expression by combining like terms and using the fact that 𝑖^2 = -1: x^2 - x - 6𝑖x - x + 1 + 6𝑖 - 6𝑖x + 6𝑖 - 36 = x^2 - 2x + 1 - 36 = x^2 - 2x - 35.Verify Standard Form: Verify that the polynomial is in standard form with a leading coefficient of 1: The polynomial x^2 - 2x - 35 is in standard form with a leading coefficient of 1.

Write a polynomial of least degree with real coefficients and with the root $1-6i$ .

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Write a polynomial of least degree with real coefficients and with the root $1-6i$ .