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Polynomial Question

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Jimbo123:
Hi all,

Could somebody help me pls with this Question

When a polynomial P(x) is divided by x^2 − 5, the remainder is x + 4. Find the remainder when
P(x) + P(−x) is divided by x^2 − 5.

Any help is much appreciated.

jamonwindeyer:
Hey! From the question we know that:



Now if we instead consider P(x) + P(-x):



In this form, where we know the remainder is just some added term, it is clear that the remainder is 8! :)

pariselle.hughes:
Heyyyy peeps... can someone please help me with this question. (First post.. so not sure where exactly to post it :))
'for what real values of 'k' does the equation x^3-2x^2-4x+k = 0 has at least one root strictly between -2 and 0??'

Thanks awesome humans!!

S200:

--- Quote from: pariselle.hughes on June 02, 2019, 09:53:21 pm ---Heyyyy peeps... can someone please help me with this question. (First post.. so not sure where exactly to post it :))
'for what real values of 'k' does the equation x^3-2x^2-4x+k = 0 has at least one root strictly between -2 and 0??'

Thanks awesome humans!!

--- End quote ---
Well you posted it in the right place...  ;)

What sort of steps have you tried already?

pariselle.hughes:
I tried using the discriminant... I really have no idea what I am doing. I am actually asking this question for a friend  ???

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