document.write( "Question 382921: use long division to find the quotient when 2x^5+4x^4-x^3-x^2+7 is divided by 2x^2-1 \n" ); document.write( "
Algebra.Com's Answer #271306 by CharlesG2(834)\"\" \"About 
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use long division to find the quotient when 2x^5+4x^4-x^3-x^2+7 is divided by 2x^2-1\r
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\n" ); document.write( "\n" ); document.write( "synthetic division
\n" ); document.write( "..............x^3 + 2x^2 + (1/2)
\n" ); document.write( "2x^2 - 1 --> 2x^5 + 4x^4 - x^3 - x^2 + 0x + 7
\n" ); document.write( ".............2x^5 + 0x^4 - x^3
\n" ); document.write( "....................4x^4 + 0x^3 - x^2
\n" ); document.write( "....................4x^4 + 0x^3 - 2x^2
\n" ); document.write( "...................................x^2 + 0x + 7
\n" ); document.write( "...................................x^2 + 0x - (1/2)
\n" ); document.write( "............................................(15/2)\r
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\n" ); document.write( "\n" ); document.write( "x^3 + 2x^2 + (1/2) + 15/(2 * (2x^2 - 1))
\n" ); document.write( "x^3 + 2x^2 + (1/2) + 15/(4x^2 - 2)
\n" ); document.write( "check:
\n" ); document.write( "(2x^2 - 1)(x^3 + 2x^2 + (1/2) + 15/(4x^2 - 2))
\n" ); document.write( "x^3(2x^2 - 1) + 2x^2(2x^2 - 1) + (1/2)(2x^2 - 1) + (15/(4x^2 - 2))(2x^2 - 1)
\n" ); document.write( "2x^5 - x^3 + 4x^4 - 2x^2 + x^2 - (1/2) + (15/2)
\n" ); document.write( "2x^5 + 4x^4 - x^3 - x^2 + (14/2)
\n" ); document.write( "2x^5 + 4x^4 - x^3 - x^2 + 7, yes
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