document.write( "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.
\n" ); document.write( "f(x)=2x^6-4x^5+2x²+7x-6\r
\n" ); document.write( "\n" ); document.write( "please help me thank you. \n" ); document.write( "
Algebra.Com's Answer #321567 by lwsshak3(11628)\"\" \"About 
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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.
\n" ); document.write( "f(x)=2x^6-4x^5+2x²+7x-6.
\n" ); document.write( "...
\n" ); document.write( "The Remainder Theorem states that: When a polynomial f(x) is divided by (x-r), the remainder is f(r).
\n" ); document.write( "..
\n" ); document.write( "For given problem, r=2
\n" ); document.write( "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.)
\n" ); document.write( "(2x^6-4x^5+2x²+7x-6)/(x-2)=x^5-2x^2+11x plus 16 (Remainder)
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\n" ); document.write( "f(2)=2*64-4*32+2*4+7*2-6
\n" ); document.write( "f(2)=128-128+8+14-6=16
\n" ); document.write( "..
\n" ); document.write( "The Factor Theorem states that if (x-r) is a factor of f(x), then f(r)=0
\n" ); document.write( "We found f(2)=16, so (x-2) is not a factor of f(x) \n" ); document.write( "
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