Question 468608: 3. Use the remainder theorem to find the remainder when f(x) is divided by x-2 . Then use the factor theorem to determine whether x-2 is a factor of f(x). Please show all of your work.
f(x)=2x^6-4x^5+2x²+7x-6
please help me thank you.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 3. Use the remainder theorem to find the remainder when f(x) is divided by x-2 . Then use the factor theorem to determine whether x-2 is a factor of f(x). Please show all of your work.
f(x)=2x^6-4x^5+2x²+7x-6.
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The Remainder Theorem states that: When a polynomial f(x) is divided by (x-r), the remainder is f(r).
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For given problem, r=2
Divide f(x) by (x-2) by long division or synthetic division. (sorry, I don't have the means to show you how to do this.)
(2x^6-4x^5+2x²+7x-6)/(x-2)=x^5-2x^2+11x plus 16 (Remainder)
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f(2)=2*64-4*32+2*4+7*2-6
f(2)=128-128+8+14-6=16
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The Factor Theorem states that if (x-r) is a factor of f(x), then f(r)=0
We found f(2)=16, so (x-2) is not a factor of f(x)
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