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[Pre-calculus]Remainder Theorem


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#1 SpeedyTheSnail

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Posted 15 July 2014 - 20:18

Well I am stuck on this math problem, and I have a feeling it is incomplete (and I don't understand it). People here seem to be very smart so I'll ask (Not for the answer but how to perform it):

 

You divide the polynomial f(x) by 

(x  2)

 and obtain a remainder of 8. What is f(2)?

 

From my book:

If a polynomial f(x) is divided by x-k, then the remainder is

r=f(k)

 

So the only think I have right now:

 

8=f(2)




#2 OP SpeedyTheSnail

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Posted 16 July 2014 - 02:43

*bump*



#3 lamminium

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Posted 16 July 2014 - 13:49

Correct.

 

To further explain the concept in simple terms:

 

Divide number 15 by 7, the answer is 2 with remainder 1.

 

The number can, thus, be written as 15 = 7 * 2 +1

 

Similarly, a polynomial P(x), when divided by (x - 2), gives a polynomial Q(x) and a remainder of 8.

 

Hence, P(x) = Q(x) * (x-2) + 8

 

Substituting x = 2 into the above, we have P(2) = Q(2) * (2 - 2) + 8 = Q(2) * 0 + 8 = 8.

 

This illustrates how the remainder theorem works.



#4 OP SpeedyTheSnail

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Posted 17 July 2014 - 00:17

Thank you!! I understand better now!



#5 Gerowen

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Posted 21 July 2014 - 03:35

I'm glad somebody understands that stuff, lol.

 

Whenever I see calculus, the only answer I can think of is 42.

 

I can build a porch, a chicken house, a people house to code, I can figure out how many square feet of carpeting I need to cover a room, or how much lumber I need to build that room.  I can load my flatbed trailer so that 60% of the weight is on the tongue, keeping the drive tires of the truck from being lifted up on, but not so much weight that I go over the tongue weight limit, and I can even re-build the engine on my pickup truck, but whenever I see stuff like that, my brain just goes DEEEEEERRRRRP!