SOLUTION: Show that 𝑥 − 𝑐 is not a factor of 𝑓(𝑥) for any real number. Let 𝑓(𝑥) = −𝑥^4 − 3𝑥^2 −2.
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Question 1188724: Show that 𝑥 − 𝑐 is not a factor of 𝑓(𝑥) for any real number. Let 𝑓(𝑥) = −𝑥^4 − 3𝑥^2 −2.
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
\ =\ -x^4\ -\ 3x^2\ -\ 2)
\ =\ -\(x^4\ +\ 3x^2\ +\ 2\))
Let 
\ =\ -\(u^2\ +\ u\ +\ 2\))
\ =\ -(u\ +\ 1)(u\ +\ 2))
\ =\ -(x^2\ +\ 1)(x^2\ +\ 2))
Let 
, then the factors of 
are:
(1)(1)}}{2})
and
(1)(1)}}{2})
Which is to say:
Similarly the factors of 
are 
and 
Therefore
John
My calculator said it, I believe it, that settles it
From
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