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avatar+294 

Factor the polynomial function over the complex numbers.

 

f(x)=x^4+9x^3+15x^2+9x+14

 Oct 23, 2018
 #1
avatar+738 
+12

Hi, this question has been asked before. 

 

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

 

Thanks!

 Oct 23, 2018
 #2
avatar+103148 
+3

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)

 

 

cool cool cool

 Oct 24, 2018

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