write in factored form: P(x)=3x^5−2x^4+64x^3−40x^2−275x+250 and that 5i is a zero

Question

Given P(x)=3x^5−2x^4+64x^3−40x^2−275x+250 and that 5i is a zero, write P in factored form as a product of linear factors.

Answer 1

(3 x - 5) (x - 1) (x + 2) (x^2 + 25)
the first three roots are real and the last one has two imaginary roots in it due to the fast that id u take a square root of a number, u should consider both possibilities of the outcome that is positive or negative. Hense five roots for a fifth degree polynomial. 

Answer 2

(x - 5i)(x + 5i) are two of the factors.

Use long division to determine other three factors.