Polynomial Question

[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]

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!!

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 

[r1ckworthy]

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!!

Hey!!! Here is my solution of the question:


BTW that cross between the f(-2) and f(0) towards the end is just multiplying the two functions together.
Yeah, like S200 mentioned, just post on the 3U Maths Question Thread anytime you have a question, so it's much more cleaner in terms of organisation, and others can also see and learn from your question