August 19, 2019, 01:44:54 am

### AuthorTopic: Polynomial Question  (Read 194 times) Tweet Share

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#### Jimbo123

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##### Polynomial Question
« on: May 04, 2019, 03:20:07 am »
0
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

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##### Re: Polynomial Question
« Reply #1 on: May 04, 2019, 09:00:24 am »
+3
Hey! From the question we know that:

$P(x)=Q(x)(x^2-5)+(x+4)$

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

$P(x)+P(-x)=Q(x)(x^2-5)+(x+4) + Q(-x)(x^2-5)+(-x+4)\\=\left(Q(x)+Q(-x)\right)(x^2-5)+8$

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

#### pariselle.hughes

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##### Re: Polynomial Question
« Reply #2 on: June 02, 2019, 09:53:21 pm »
+1
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

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##### Re: Polynomial Question
« Reply #3 on: June 02, 2019, 09:59:07 pm »
+1
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?
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#### pariselle.hughes

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##### Re: Polynomial Question
« Reply #4 on: June 02, 2019, 10:19:20 pm »
+1
I tried using the discriminant... I really have no idea what I am doing. I am actually asking this question for a friend

#### r1ckworthy

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##### Re: Polynomial Question
« Reply #5 on: June 02, 2019, 10:45:51 pm »
+1
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
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