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Factor the polynomial function over the complex numbers

f(x)=x^4−x^3−2x−4

 Nov 1, 2018

Best Answer 

 #1
avatar+6252 
+2

f(x)=x4x32x4I like to quickly check for rational roots before getting fancypossible roots here are x=±1,±2,±4and a quick check shows that x=1, 2 are actual rootswe can then do the polynomial division to find thatf(x)=(x+1)(x2)(x2+2)and complete the factoring asf(x)=(x+1)(x2)(x+i2)(xi2)

 

Another way of approaching this is to see if you get lucky when factoring pieces of it.

 

x4x32x4=(x44)(x3+2x)=(x22)(x2+2)x(x2+2)=(x2+2)(x2x2)=(x2+2)(x2)(x+1)=(x+i2)(xi2)(x2)(x+1)which is the same as the first answer with the factors listed in different orders

 

The second method is certainly faster if you get lucky.

 Nov 1, 2018
 #1
avatar+6252 
+2
Best Answer

f(x)=x4x32x4I like to quickly check for rational roots before getting fancypossible roots here are x=±1,±2,±4and a quick check shows that x=1, 2 are actual rootswe can then do the polynomial division to find thatf(x)=(x+1)(x2)(x2+2)and complete the factoring asf(x)=(x+1)(x2)(x+i2)(xi2)

 

Another way of approaching this is to see if you get lucky when factoring pieces of it.

 

x4x32x4=(x44)(x3+2x)=(x22)(x2+2)x(x2+2)=(x2+2)(x2x2)=(x2+2)(x2)(x+1)=(x+i2)(xi2)(x2)(x+1)which is the same as the first answer with the factors listed in different orders

 

The second method is certainly faster if you get lucky.

Rom Nov 1, 2018
 #2
avatar+234 
0

thank you

skye25  Nov 1, 2018

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