Use the given zero to find the remaining zeros of the polyno

Use the given zero to find the remaining zeros of the polynomial function. (Enter you P(x) = X^4 - 6x^3 + 47X^2 - 98x + 290; 2 + 5i

P(x) = x^4 - 6x^3 + 47 x^2 - 98x + 290

one zero is 2+5i

since complex zeros occur in pairs other zero would be 2 - 5i

( x - (2+5i)) ( x-(2-5i)) = x^2 - 4x +29

dividing the polynomial by x^2 - 4x +29

x^4 - 6x^3 + 47 x^2 - 98x + 290 / x^2 - 4x +29 = x^2 - 2x +10

setting x^2 - 2x +10 =0 and solving for x

x = 1-3i

x = 1+ 3i

remaining zeros are

x = 2 - 5i , 1+3i , 1-3i