We need a matching complex to 2+3i. The conjugate is 2-3i and the two factors are (x-2-3i)(x-2+3i)=(x²-4x+4+9)=x²-4x+13. The polynomial is (x-4)(x+8)(x²-4x+13)=(x²+4x-32)(x²-4x+13)= x⁴-4x³+13x² +4x³-16x²+ 52x -32x²+128x-416 x⁴-35x²+180x-416 is the 4th degree polynomial.