Question 641566: ACC
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Use the remainder theorem to find the remainder when f(x) is divided by 2. then use the factor theorem?
use the remainder theorem to find the remainder when f(x) is divided by 2. then use the factor theorem to determine whether x+2 is a factor of f(x)
f(x)=2x^6-8x^4+x3-20
Remainder is?
is x+2 a factor of f(x)?
i tried to have a tutor help me and she confused me even more after she said she doesnt really know what she is doing! please help me n show the work too...soo lost
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! The remainder theorem is this:
if you divide f(x) by x-t and you get some remainder 'r', then f(t) = r
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In this case, x+2 is really x-(-2) which matches with x-t. So t = -2
We can use the theorem in reverse to get
f(x)=2x^6-8x^4+x^3-20
f(-2)=2(-2)^6-8(-2)^4+(-2)^3-20
f(-2)=2(64)-8(16)-8-20
f(-2)=128-128-8-20
f(-2)=-28
So if you divide 2x^6-8x^4+x^3-20 by x+2, then you get a remainder of -28
Since this remainder is NOT zero, this means that x+2 is NOT a factor of f(x)=2x^6-8x^4+x^3-20
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