Question

Write a polynomial function in standard form with minimal degree that has root -1 and root -3-i

Answer 1

when there is an unreal root -3-i, there is also an unreal root -3+i
(x+1)[x-(-3-i)][x-(-3+i)]
(x+1)[(x+3)+i)][(x+3)-i)]
(x+1)[(x+3)²-i²]
(x+1)(x²+6x+9+1)
(x+1)(x²+6x+10)
Expand: x³+6x²+10x+x²+6x+10
x³+7x²+16x+10 is the final answer.