document.write( "Question 458026: When ax^3-2x^2+3x-5 is divided by 2x-1, the remainder is -8
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Algebra.Com's Answer #314444 by Edwin McCravy(20060) $\"\"$ $\"About$

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When ax^3-2x^2+3x-5 is divided by 2x-1, the remainder is -8
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document.write( "2x - 1)ax³ - 2x² - 2x² + 3x - 5\r\n" );
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document.write( "We won't divide that out, but suppose we did.\r\n" );
document.write( "We would get some quotient Q(x) and a remainder of -8\r\n" );
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document.write( "                Q(x)            \r\n" );
document.write( "2x - 1)ax³ - 2x² - 2x² + 3x - 5\r\n" );
document.write( "         ..... \r\n" );
document.write( "           ......\r\n" );
document.write( "                        _______\r\n" );
document.write( "                             -8\r\n" );
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document.write( "Then use \r\n" );
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document.write( "               DIVIDEND = QUOTIENT*DIVISOR + REMAINDER\r\n" );
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document.write( "     ax³ - 2x² + 3x - 5 = Q(x)*(2x - 1) + (-8)\r\n" );
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document.write( "We want to make the factor (2x - 1) equal to zero so that\r\n" );
document.write( "term will be eliminated. \r\n" );
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document.write( "2x - 1 = 0\r\n" );
document.write( "    2x = 1\r\n" );
document.write( "     x = ½\r\n" );
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document.write( "Now substitute x = ½  in\r\n" );
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document.write( "     ax³ - 2x² + 3x - 5 = Q(x)*(2x - 1) + (-8)\r\n" );
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document.write( "     a(½)³ - 2(½)² + 3(½) - 5 = Q(½)*(2*½ - 1) + (-8)\r\n" );
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document.write( "     a(⅛) - 2(¼) +  - 5 = Q(½)*(1 - 1) - 8\r\n" );
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document.write( "     - ½ +  - 5 = Q(½)*(0) - 8\r\n" );
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document.write( "     - ½ +  - 5 = 0 - 8\r\n" );
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document.write( "     - ½ +  - 5 = -8\r\n" );
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document.write( "Clear of fractions by multiplying through by 8\r\n" );
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document.write( "         a - 4 + 12 - 40 = -64\r\n" );
document.write( "                  a - 32 = -64\r\n" );
document.write( "                       a = -32    \r\n" );
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document.write( "Checking:    \r\n" );
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document.write( "              -16x² - 9x - 3 \r\n" );
document.write( "2x - 1)-32x³ -  2x² + 3x - 5\r\n" );
document.write( "       -32x³ + 16x²\r\n" );
document.write( "              -18x² + 3x\r\n" );
document.write( "              -18x² + 9x\r\n" );
document.write( "                     -6x - 5\r\n" );
document.write( "                     -6x + 3\r\n" );
document.write( "                          -8    \r\n" );
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document.write( "It leaves the remainder -8, so we are correct!\r\n" );
document.write( "Edwin

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