document.write( "Question 465061: use the factor theorem to determine whether (x-3) is a factor of
\n" ); document.write( "f(x) = x⁴+ 12x³ + 6x + 27
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Algebra.Com's Answer #318668 by Edwin McCravy(20055) $\"\"$ $\"About$

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use the factor theorem to determine whether (x-3) is a factor of
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document.write( "The factor theorem says that to find out whether A is a factor of B,\r\n" );
document.write( "you divide B by A and if you get a zero remainder then A is a factor\r\n" );
document.write( "of B but if you don't get a zero remainder, then A is not a factor of B.\r\n" );
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document.write( "We want to find out whether (x-3) is a factor of f(x) = x⁴+ 12x³ + 6x + 27,\r\n" );
document.write( "so we divide x^4+12x^3+6x+27 by (x-3) to see if we get a zero remainder:\r\n" );
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document.write( "    x - 3)x⁴+ 12x³ + 0x² + 6x + 27\r\n" );
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document.write( "Notice there was no x² term so we had to insert +0x².\r\n" );
document.write( "But we have a shortcut way of doing that called \"synthetic\r\n" );
document.write( "division\".  We change the sign of the -3 to +3 and write:\r\n" );
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document.write( "       3|1  12   0   6   27\r\n" );
document.write( "        |    3  45 135  423   \r\n" );
document.write( "         1  15  45 141  450\r\n" );
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document.write( "So we got 450, not 0. That means that (x-3) is not a factor of\r\n" );
document.write( "x⁴+ 12x³ + 6x + 27\r\n" );
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document.write( "Edwin

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