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# Remainder theorem?

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9 I need to solve this by using the remainder theorem thing. I don't know the remainder theorem. I tried looking it up but I didn't understand. Are there two different ways to solve using the remainder theorem? Please show work. Sorry. Thank you.

Sep 18, 2019

#1
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Here is one way (do not know if this is remainder theorem though) Sep 18, 2019
#2
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Now I understand it better. I tried looking it up but it would just confuse me more. Thank you for your help.

Guest Sep 19, 2019
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Thanks EP

EP has done it the long way but that is not the remainder theorem.

The remainder theorem might be difficult to understand but it is very simple to use.

The remainder theorem says that if  f(x) is divided by  (x-k) then the ramainder will be  f(k)

in this case k=-4

so the remainder will be

f(-4)

f(-4)=-64+128+6 = 70

The remainder is just the 70 not  70/(x+4)

Simple view

the zero of (x+4) is -4    therefore   g(-4) will give the remainder when g(x) is divided by (x+4)

Sep 19, 2019
#4
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Ooops sorry......   The remainder is of course just 70.    If you divide out the entire thing you would have a term of  70/(x+4)   i.e.

(x+4)  *  { x^2 +4x-16 + 70/(x+4)  }  = x^3 + 8x^2 +6            sorry I took it toooo far !

ElectricPavlov  Sep 19, 2019
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Melody  Sep 19, 2019
#6
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Lol, CPhill is catching up to you, Melody!

CalculatorUser  Sep 19, 2019
#7
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I'm not OP but I do have a similar question to this that I'm stuck on. Do I solve a question like this using what EP used or do I do it like Melody or do I have to do both to find the answer?

Guest Sep 19, 2019
#8
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You can use either method....whichever the Q asks you t use....

ElectricPavlov  Sep 19, 2019
#9
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Okay. Great. Thanks for answering. Have a great day.

Guest Sep 19, 2019