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# HELP!

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What are the zeros of the polynomial function?

f(x)=x4+2x3−16x2−2x+15

−5

−1

0

1

3

5

Nov 2, 2018

#1
+18849
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Here is a graphical solution:

Nov 2, 2018
#2
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Thanks! I need help on this quesiton

Factor the polynomial function over the complex numbers.

f(x)=x4−x3−2x−4

f(x) =

Nov 2, 2018
#3
+102948
+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

Nov 2, 2018
#4
0

Thanks!! could you help me with this question?

Factor the polynomial function over the complex numbers.

f(x)=x4−x3−2x−4

Nov 2, 2018
#5
+102948
+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)

Nov 2, 2018
#6
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THANK YOU SO MUCH!

Nov 2, 2018