Factor the polynomial function over the complex numbers.

Hi, this question has been asked before. 

https://web2.0calc.com/questions/factor-the-polynomial-function-over-the-complex-number

Thanks!

x^4  + 9x^3  + 15x^2  + 9x + 14

We can use a factoring "trick" here....write this as

x^4 +  9x^3 + 14x^2  + x^2  + 9x  + 14     factor by grouping

x^2 ( x^2 + 9x + 14)  +  1 ( x^2 + 9x + 14)

(x^2 + 1) (x^2 + 9x + 14)

(x^2 + 1) (x+ 7) ( x + 2)

(x + 1i) ( x - 1i) (x+ 7) ( x + 2)