Answer:
x^4 - 15x^2 - 38x - 60.
Step-by-step explanation:
Writing it in factor form:
( x - 5)(x + 3) ( x - (-1 + 2i) )(x - (-1 - 2i))
There are 4 parentheses because complex roots occur in pairs.
( x - (-1 + 2i) )(x - (-1 - 2i))
= ( x + 1 - 2i) )(x +1 + 2i))
= x^2 + x + 2ix + x + 1 + 2i - 2ix - 2i + 4
= x^2 + 2x + 4.
So our polynomial is
( x - 5)(x + 3)( x^2 + 2x + 4)
= (x^2 - 2x - 15)(x^2 + 2x + 4)
= x^4 + 2x^3 + 4x^2 - 2x^3 - 4x^2 - 8x - 15x^2 - 30x - 60
= x^4 - 15x^2 - 38x - 60.
