Question

Write a polynomial function of least degree with integral coefficients that has the given zeros. –2, –3,3 – 6i

Answer 1

$(x-(-2))(x-(-3))(x-(3-6i)(x-(3+6i))=\\(x+2)(x+3)(x-3+6i)(x-3-6i)=\\(x^2+3x+2x+6)((x-3)^2+36)=\\(x^2+5x+6)(x^2-6x+9+36)=\\(x^2+5x+6)(x^2-6x+45)=\\x^4-6x^3+45x^2+5x^3-30x^2+225x+6x^2-36x+270=\\x^4-x^3+21x^2+189x+270$