Question 710827: Hi, I am working on finding the zeros of a polynomial function and don't understand it. I also don't have access to a calculator right now. I need help on this problem: f(x) = x^4 + x^3 + 2x^2 + 4x - 8. To find all zeros of the polynomial function, I know that I would have to use synthetic division but where do I start? Thanks!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! f(x) = x^4 + x^3 + 2x^2 + 4x - 8. To find all zeros of the polynomial function,
Use the factors of -8, to perform synthetic division, how about x=-2
:
. . .__________________
-2 | 1 + 1 + 2 + 4 - 8
.. . . . . -2 + 2 - 8 + 8
. . -------------------
. . . 1 - 1 + 4 - 4 + 0
:
we now have (x + 2)(x^3 - x^2 + 4x - 4)
we could us synthetic division again but this will group factor
(x^3 - x^2) + (4x - 4)
x^2(x - 1) + 4(x - 1)
Factor out (x-1)
(x - 1)(x^2 + 4)
now we have
(x + 2)(x - 1)(x^2 + 4)
only two real solutions
x = -2
x = +1
:
I did confirm this on my calculator
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