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What are the zeros of the polynomial function?

f(x)=x4+2x3−16x2−2x+15


Select each correct answer.

 

−5

−1

0

1

3

5

 Nov 2, 2018
 #1
avatar+17332 
+1

Here is a graphical solution:

 

 

 Nov 2, 2018
 #2
avatar
0

Thanks! I need help on this quesiton

 

Factor the polynomial function over the complex numbers.

 

f(x)=x4−x3−2x−4

 

Enter your answer in the box.

f(x) = 

 Nov 2, 2018
 #3
avatar+98182 
+1

x^4+2x^3−16x^2−2x+15

 

Note  that we can use a special  "trick" to write this in a slightly different manner

This will make the polynomial easily "factorable"

[ P.S.  - This does not always work...but it just happens to, here  ]

 

(x^4 + 2x^3 - 15x^2) - ( x^2 + 2x -15)    factor

 

x^2 ( x^2 + 2x - 15) - 1 ( x^2 + 2x - 15)   

 

(x^2 - 1) ( x^2 + 2x - 15)

 

(x + 1) ( x - 1) ( x + 5) ( x - 3)

 

Setting each factor to 0  and solving for x  gives the roots  (zeros)

 

x =  - 1 ,  x  = 1  ,   x = -5     x  =  3

 

 

 

cool cool cool

 Nov 2, 2018
 #4
avatar
0

Thanks!! could you help me with this question?

 

Factor the polynomial function over the complex numbers.

 

f(x)=x4−x3−2x−4

 

Enter your answer in the box.

 Nov 2, 2018
 #5
avatar+98182 
+1

Factor the polynomial function over the complex numbers.

 

f(x)=x^4−x^3−2x−4

 

We can write this in a slighly different manner

 

x^4 - 4 - x^3 - 2x

 

(x^4 - 4)  - x(x^2 + 2)

 

(x^2 - 2) (x^2 + 2)  -  x(x^2 + 2)      take out the common factor, x^2 + 2

 

(x^2 + 2)  [ x^2 - 2 - x ]

 

( x^2 + 2) ( x^2 - x - 2)

 

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

 

 

 

cool cool cool

 Nov 2, 2018
 #6
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0

THANK YOU SO MUCH!

 Nov 2, 2018

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